How to divide exponents - PSAT Math

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Question

5. Simplify the problem (x4y2/x5)3

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Answer

Properties of exponents suggests that when multiplying the same base, add the exponents, when dividing, subtract the exponents on bottom from those on top, and when raising an exponent to another power, multiply the exponents. Remember that (x4/x5) = x–1 = 1/x; Still using order of operations (PEMDAS) we get the following:(x4y2/x5)3= (y2/x)3 = y6/(x3).

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Question

For all real numbers n, (2_n_ * 2) / (2_n_ * 2_n_) =

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Answer

(2_n_ * 2) / (2_n_ * 2_n_) simplifies to 2/2_n_ or 21/2_n_.

When dividing exponents with the same base, you subtract the divisor from the dividend, giving 21–n.

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Question

If x9/x3 = xn, solve for n.

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Answer

When dividing terms with the same base, we can subtract the exponents:

9 – 3 = 6

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Question

If $c\neq 0$ , then $\frac{(c^3)^2}{c^2c^4}=?$

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Answer

Start by simplifying the numerator and denominator separately. In the numerator, (c3)2 is equal to c6. In the denominator, c2 * c4 equals c6 as well. Dividing the numerator by the denominator, c6/c6, gives an answer of 1, because the numerator and the denominator are the equivalent.

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Question

Simplify the following expression: (x2y4)/(x3y3z2)

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Answer

According to the rules of exponents, ax/ay = ax-y

In this expression, we can follow this rule to simplify x2/x3 and y4/y3

x2–3 = x–1 = 1/x. y4–3 = y1 = y.

Therefore, y/xz2

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Question

Simplify:

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Answer

When dividing, subtract exponents (xa/xb = x(a – b).) Therefore, the quantity in the parenthesis is: x(4 – (–2)) * y(–3 – (–3)) * z(–1 – 5) = x6/z6. Raising this to the 3/2 power results in multiplying the exponents by 3/2: x6 * 3/2/z6 * 3/2 = x9/z9.

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Question

Half of the radioactive nuclei of a substance decays in a week. If a sample started with 1010 nuclei, how many have decayed after 28 days?

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Answer

If half of the sample decays each week: 1/2 is left after one week, 1/4 is left after two weeks, 1/8 is left after three weeks and 1/16 is left after four weeks (28 days.) That means that 15/16 has decayed. 15/16 x 1010 = 9. 375 x 109

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Question

If $a\not\equiv0$ , which of the following is equal to $\frac{(a^6*a^2)^3}{a^6}$ ?

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Answer

The numerator is simplified to (by adding the exponents), then cube the result. a24/a6 can then be simplified to $a^{18}$ .

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Question

Simplify x2x4y/y2x

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Answer

According to the rules of exponents, one can add the exponents when adding to variables with the same base. So, x2x4 becomes x6.

The rules of exponents also state that if the bases are the same, one can substract the exponents when dividing. So, x6/x becomes x5. Similarly, y/y2 becomes 1/y.

When combining these operations, one gets x5/y.

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Question

54 / 25 =

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Answer

25 = 5 * 5 = 52. Then 54 / 25 = 54 / 52.

Now we can subtract the exponents because the operation is division. 54 / 52 = 54 – 2 = 52 = 25. The answer is therefore 25.

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Question

Simplify

$\dpi{100} \small \frac{20x^{4}y^{-3}z^{2}}{5z^{-1}y^{2}x^{2}}=$

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Answer

Divide the coefficients and subtract the exponents.

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Question

Which of the following is equal to the expression , where

xyz ≠ 0?

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Answer

(xy)4 can be rewritten as x4y4 and z0 = 1 because a number to the zero power equals 1. After simplifying, you get 1/y.

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Question

$\dpi{100} \small \frac{7^{10}-7^{8}}{7^{9}-7^{7}}=$

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Answer

The easiest way to solve this is to simplify the fraction as much as possible. We can do this by factoring out the greatest common factor of the numerator and the denominator. In this case, the GCF is .

$\frac{7^7\left ( 7^3-7^1\right)}{7^7\left ( 7^2-1\right)}$

Now, we can cancel out the from the numerator and denominator and continue simplifying the expression.

$\frac{7^7\left ( 7^3-7^1\right)}{7^7\left ( 7^2-1\right)}=\frac{7^3-7^1}{7^2-1}=\frac{343-7}{49-1}=\frac{336}{48}=7$

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Question

54 / 25 =

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Answer

25 = 5 * 5 = 52. Then 54 / 25 = 54 / 52.

Now we can subtract the exponents because the operation is division. 54 / 52 = 54 – 2 = 52 = 25. The answer is therefore 25.

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Question

$\frac{55^{10}}{121^6} \cdot \frac{11^8}{5^{8}} = ?$

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Answer

The key to this problem is understanding how exponents divide. When two exponents have the same base, then the exponent on the bottom can simply be subtracted from the exponent on top. I.e.:

$\frac{5^x}{5^y} = 5^{x-y}$

Keeping this in mind, we simply break the problem down into prime factors, multiply out the exponents, and solve.

$\frac{55^{10}}{121^6} \cdot \frac{11^8}{5^8} = \frac{(5\cdot 11)^{10}}{5^8}\cdot \frac{11^8}{(11\cdot11)^6} = 11^{10}\cdot\frac{5^{10}}{5^8} \cdot \frac{11^8}{11^{12}} = 5^2 \cdot \frac{11^{10+8}}{11^{12}} = 5^2\cdot11^6$

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Question

For all real numbers n, (2_n_ * 2) / (2_n_ * 2_n_) =

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Answer

(2_n_ * 2) / (2_n_ * 2_n_) simplifies to 2/2_n_ or 21/2_n_.

When dividing exponents with the same base, you subtract the divisor from the dividend, giving 21–n.

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Question

If x9/x3 = xn, solve for n.

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Answer

When dividing terms with the same base, we can subtract the exponents:

9 – 3 = 6

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Question

If $c\neq 0$ , then $\frac{(c^3)^2}{c^2c^4}=?$

Tap to reveal answer

Answer

Start by simplifying the numerator and denominator separately. In the numerator, (c3)2 is equal to c6. In the denominator, c2 * c4 equals c6 as well. Dividing the numerator by the denominator, c6/c6, gives an answer of 1, because the numerator and the denominator are the equivalent.

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Question

Simplify the following expression: (x2y4)/(x3y3z2)

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Answer

According to the rules of exponents, ax/ay = ax-y

In this expression, we can follow this rule to simplify x2/x3 and y4/y3

x2–3 = x–1 = 1/x. y4–3 = y1 = y.

Therefore, y/xz2

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How to divide exponents - PSAT Math

5. Simplify the problem (x4y2/x5)3

For all real numbers n, (2_n_ * 2) / (2_n_ * 2_n_) =

(2_n_ * 2) / (2_n_ * 2_n_) simplifies to 2/2_n_ or 21/2_n_. When dividing exponents with the same base, you subtract the divisor from the dividend, giving 21–n.

If x9/x3 = xn, solve for n.

When dividing terms with the same base, we can subtract the exponents: 9 – 3 = 6

If , then

Start by simplifying the numerator and denominator separately. In the numerator, (c3)2 is equal to c6. In the denominator, c2 * c4 equals c6 as well. Dividing the numerator by the denominator, c6/c6, gives an answer of 1, because the numerator and the denominator are the equivalent.

Simplify the following expression: (x2y4)/(x3y3z2)

According to the rules of exponents, ax/ay = ax-y In this expression, we can follow this rule to simplify x2/x3 and y4/y3 x2–3 = x–1 = 1/x. y4–3 = y1 = y. Therefore, y/xz2

Simplify:

When dividing, subtract exponents (xa/xb = x(a – b).) Therefore, the quantity in the parenthesis is: x(4 – (–2)) * y(–3 – (–3)) * z(–1 – 5) = x6/z6. Raising this to the 3/2 power results in multiplying the exponents by 3/2: x6 * 3/2/z6 * 3/2 = x9/z9.

Half of the radioactive nuclei of a substance decays in a week. If a sample started with 1010 nuclei, how many have decayed after 28 days?

If half of the sample decays each week: 1/2 is left after one week, 1/4 is left after two weeks, 1/8 is left after three weeks and 1/16 is left after four weeks (28 days.) That means that 15/16 has decayed. 15/16 x 1010 = 9. 375 x 109

If , which of the following is equal to ?

The numerator is simplified to (by adding the exponents), then cube the result. a24/a6 can then be simplified to .

Simplify x2x4y/y2x

54 / 25 =

25 = 5 * 5 = 52. Then 54 / 25 = 54 / 52. Now we can subtract the exponents because the operation is division. 54 / 52 = 54 – 2 = 52 = 25. The answer is therefore 25.

Simplify

Divide the coefficients and subtract the exponents.

Which of the following is equal to the expression , where xyz ≠ 0?

(xy)4 can be rewritten as x4y4 and z0 = 1 because a number to the zero power equals 1. After simplifying, you get 1/y.

54 / 25 =

25 = 5 * 5 = 52. Then 54 / 25 = 54 / 52. Now we can subtract the exponents because the operation is division. 54 / 52 = 54 – 2 = 52 = 25. The answer is therefore 25.

For all real numbers n, (2_n_ * 2) / (2_n_ * 2_n_) =

(2_n_ * 2) / (2_n_ * 2_n_) simplifies to 2/2_n_ or 21/2_n_. When dividing exponents with the same base, you subtract the divisor from the dividend, giving 21–n.

If x9/x3 = xn, solve for n.

When dividing terms with the same base, we can subtract the exponents: 9 – 3 = 6

If , then

Start by simplifying the numerator and denominator separately. In the numerator, (c3)2 is equal to c6. In the denominator, c2 * c4 equals c6 as well. Dividing the numerator by the denominator, c6/c6, gives an answer of 1, because the numerator and the denominator are the equivalent.

Simplify the following expression: (x2y4)/(x3y3z2)

According to the rules of exponents, ax/ay = ax-y In this expression, we can follow this rule to simplify x2/x3 and y4/y3 x2–3 = x–1 = 1/x. y4–3 = y1 = y. Therefore, y/xz2

(2_n_ * 2) / (2_n_ * 2_n_) simplifies to 2/2_n_ or 21/2_n_.

When dividing exponents with the same base, you subtract the divisor from the dividend, giving 21–n.

When dividing terms with the same base, we can subtract the exponents:

9 – 3 = 6

If $c\neq 0$ , then $\frac{(c^3)^2}{c^2c^4}=?$

According to the rules of exponents, ax/ay = ax-y

In this expression, we can follow this rule to simplify x2/x3 and y4/y3

x2–3 = x–1 = 1/x. y4–3 = y1 = y.

Therefore, y/xz2

If $a\not\equiv0$ , which of the following is equal to $\frac{(a^6*a^2)^3}{a^6}$ ?

The numerator is simplified to (by adding the exponents), then cube the result. a24/a6 can then be simplified to $a^{18}$ .

25 = 5 * 5 = 52. Then 54 / 25 = 54 / 52.

Now we can subtract the exponents because the operation is division. 54 / 52 = 54 – 2 = 52 = 25. The answer is therefore 25.

Simplify

$\dpi{100} \small \frac{20x^{4}y^{-3}z^{2}}{5z^{-1}y^{2}x^{2}}=$

Which of the following is equal to the expression , where

xyz ≠ 0?

25 = 5 * 5 = 52. Then 54 / 25 = 54 / 52.

Now we can subtract the exponents because the operation is division. 54 / 52 = 54 – 2 = 52 = 25. The answer is therefore 25.

(2_n_ * 2) / (2_n_ * 2_n_) simplifies to 2/2_n_ or 21/2_n_.

When dividing exponents with the same base, you subtract the divisor from the dividend, giving 21–n.

When dividing terms with the same base, we can subtract the exponents:

9 – 3 = 6

If $c\neq 0$ , then $\frac{(c^3)^2}{c^2c^4}=?$

According to the rules of exponents, ax/ay = ax-y

In this expression, we can follow this rule to simplify x2/x3 and y4/y3

x2–3 = x–1 = 1/x. y4–3 = y1 = y.

Therefore, y/xz2