Distributing Exponents (Power Rule) - Algebra II

Card 0 of 484

Question

Evaluate:

Answer

When an exponent is being raised by another exponent, we just multiply the powers and keep the base the same. However, with a number present, we need to also apply the exponent to the number. We essentially breakdown the components as such: .

$(4x^3)^3=4^3x^{3*3}=64x^9$

Compare your answer with the correct one above

Question

Evaluate: $(6x^{-3})^{2}$

Answer

When an exponent is being raised by another exponent, we just multiply the powers and keep the base the same. However, with a number present, we need to also apply the exponent to the number. We essentially breakdown the components as such: .

$(6x^{-3})^{2}=(\frac{6}{x^3})^{2}=\frac{36}{x^6}$

Compare your answer with the correct one above

Question

Evaluate: $(2x^3)^{-4}$

Answer

When an exponent is being raised by another exponent, we just multiply the powers and keep the base the same. However, with a number present, we need to also apply the exponent to the number. We essentially breakdown the components as such: .

$(2x^3)^{-4}=(\frac{1}{(2x^3)^4})=\frac{1}{16x^{12}}$

Compare your answer with the correct one above

Question

Evaluate: $(-3x^{-4})^{-3}$

Answer

When an exponent is being raised by another exponent, we just multiply the powers and keep the base the same. However, with a number present, we need to also apply the exponent to the number. We essentially breakdown the components as such: .

$(-3x^{-4})^{-3}=-(\frac{3}{x^4})^{-3}=-(\frac{x^4}{3})^3=-\frac{x^{12}}{27}$

Compare your answer with the correct one above

Question

What is the largest positive integer, , such that is a factor of ?

Answer

. Thus, is equal to 16.

Compare your answer with the correct one above

Question

Simplify: $9(3^{3})^{15}$

Answer

Simplify the exponent outside the exponent by use of the product rule of exponents.

$9(3^{3})^{15} =9(3^{3\cdot15}) =9(3^{45})$

Change the nine to base three.

$9(3^{45}) = 3^2(3^{45})$

Since powers of a common base are multiplied, the powers can be added.

$3^2(3^{45}) =3^{2+45}= 3^{47}$

The answer is: $3^{47}$

Compare your answer with the correct one above

Question

Simplify:

Answer

When an exponent is being raised by another exponent, we multiply the exponents and keep the base the same.

$(x^5)^7=x^{5*7}=x^{35}$

Compare your answer with the correct one above

Question

Simplify: $(x^{-4})^{-3}$

Answer

When an exponent is being raised by another exponent, we multiply the exponents and keep the base the same.

$(x^{-4})^{-3}=x^{-4*-3}=x^{12}$

Compare your answer with the correct one above

Question

Simplify:

Answer

When an exponent is being raised by another exponent, we multiply the exponents and keep the base the same. Since there is a number present, we also must perform the exponent operation as well.

$(3x^6)^5=3^5x^{56}=243x^{30}$

Compare your answer with the correct one above

Question

Simplify:

Answer

Since we have two expressions being multiplied, we follow PEMDAS meaning we do exponents first then multiplication. We will apply power rule and then multiplication rule of exponents.

$4x^2(3x^6)^2=4x^2*9x^{12}=36x^{14}$

Compare your answer with the correct one above

Question

Simplify:

Answer

Since we have two expressions being multiplied, we follow PEMDAS meaning we do exponents first then multiplication. We will apply power rule and then multiplication rule of exponents.

$5x^6(4x^2)^3=5x^6*64x^6=320x^{12}$

Compare your answer with the correct one above

Question

Simplify: $[(9^{4})^{20}]^2$

Answer

Evaluate by using the product rule of exponents. Solve the parentheses first.

$(9^{4})^{20} = 9^{4\cdot 20} =9^{80}$

Solve the bracket.

$[(9^{4})^{20}]^2=[9^{80}]^2 = 9^{80\cdot 2} =9^{160}$

The answer is: $9^{160}$

Compare your answer with the correct one above

Question

Simplify:

$\frac{(x^2y^3)^9}{xy^7}$

Answer

Recall that when an exponent is raised to another exponent, you will need to multiply the two exponents together.

Start by simplifying the numerator:

$(x^2y^3)^9=x^{18}y^{27}$

Now, place this on top of the denominator and simplify. Recall that when you divide exponents that have the same base, you will subtract the exponent in the denominator from the exponent in the numerator.

$\frac{x^{18}y^{27}}{xy^7}=x^{17}y^{20}$

Compare your answer with the correct one above

Question

Simplify: $2(2^{20})^5$

Answer

We can solve the exponent in the parentheses first.

Use the power rule to simplify the term.

$(2^{20})^5 = (2^{20\cdot 5}) = 2^{100}$

The expression becomes:

$2(2^{20})^5 = 2(2^{100}) = 2^1 \cdot 2^{100}$

Since the bases of the powers are the same, we can add the exponents.

The answer is: $2^{101}$

Compare your answer with the correct one above

Question

Simplify:

$(5^{-8})^{-12}$

Answer

When dealing with exponents being raised by another exponent, we just multiply the powers and keep the base the same.

$(5^{-8})^{-12}=5^{-8*-12}=5^{96}$

Compare your answer with the correct one above

Question

Simplify: $(3a^2b^{-3}c^4)^2$

Answer

To simplify this expression, square every term in the parentheses:

$3^2a^4b^{-6}c^8$ .

Then simplify and get rid of the negative exponent by putting the b term on the denominator:

$\frac{9a^4c^8}{b^6}$ .

Compare your answer with the correct one above

Question

Simplify:

Answer

When an exponent is raised by another exponent, we will multiply the exponents and keep the base the same.

Simplify:

$(4^7)^7=4^{7*7}=4^{49}$

Compare your answer with the correct one above

Question

Simplify:

$(8^7)^{-2}$

Answer

When an exponent is raised by another exponent, we will multiply the exponents and keep the base the same.

Simplify:

$(8^7)^{-2}=8^{7*-2}=8^{-14}$

Compare your answer with the correct one above

Question

Simplify:

$(5^{-5})^{-5}$

Answer

When an exponent is raised by another exponent, we will multiply the exponents and keep the base the same.

Simplify:

$(5^{-5})^{-5}=5^{-5*-5}=5^{25}$

Compare your answer with the correct one above

Question

Solve:

Answer

Solve each term separately. A number to the zeroth power is equal to 1, but be careful to apply the signs after the terms have been simplified.

Compare your answer with the correct one above

Tap the card to reveal the answer