Variables - Algebra

Card 0 of 5229

Question

Multiply the following monomial quotients:

$3x\cdot 2x$

Answer

To solve this problem, split it into two steps:

1. Multiply the coefficients

$3\cdot2=6$

2. Multiply the variables. We also need to remember the following laws of exponents rule: When multiplying variables, add the exponents.

$x\cdot x=x^{1+1}=x^{2}$

Combine these to get the final answer:

$6x^{2}$

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Question

Multiply the following monomial quotients:

$x^{6}\cdot x^{4}$

Answer

To solve this problem, split it into two steps:

1. Multiply the coefficients

$1\cdot1=1$

2. Multiply the variables. We also need to remember the following laws of exponents rule: When multiplying variables, add the exponents.

$x^{6}\cdot x^{4}=x^{6+4}=x^{10}$

Combine these to get the final answer:

$x^{10}$

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Question

Multiply the following monomial quotients:

$2x^{3}\cdot x^{5}=2x^{8}$

Answer

To solve this problem, split it into two steps:

1. Multiply the coefficients

$2\cdot1=2$

2. Multiply the variables. We also need to remember the following laws of exponents rule: When multiplying variables, add the exponents.

$x^{3}\cdot x^{5}=x^{3+5}=x^{8}$

Combine these to get the final answer:

$2x^{8}$

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Question

Multiply the following monomial quotients:

$x^{10}\cdot 3x$

Answer

To solve this problem, split it into two steps:

1. Multiply the coefficients

$1\cdot3=3$

2. Multiply the variables. We also need to remember the following laws of exponents rule: When multiplying variables, add the exponents.

$x^{10}\cdot x=x^{10+1}=x^{11}$

Combine these to get the final answer:

$3x^{11}$

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Question

Multiply the following monomial quotients:

$3x\cdot 6x$

Answer

To solve this problem, split it into two steps:

1. Multiply the coefficients

$3\cdot6=18$

2. Multiply the variables. We also need to remember the following laws of exponents rule: When multiplying variables, add the exponents.

$x\cdot x=x^{1+1}=x^{2}$

Combine these to get the final answer:

$18x^{2}$

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Question

Multiply the following monomial quotients:

$6x\cdot 4x^{2}$

Answer

To solve this problem, split it into two steps:

1. Multiply the coefficients

$6\cdot4=24$

2. Multiply the variables. We also need to remember the following laws of exponents rule: When multiplying variables, add the exponents.

$x\cdot x^{2}=x^{1+2}=x^{3}$

Combine these to get the final answer:

$24x^{3}$

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Question

Multiply the following monomial quotients:

$2x^{5}\cdot 3x^{2}$

Answer

To solve this problem, split it into two steps:

1. Multiply the coefficients

$2\cdot3=6$

2. Multiply the variables. We also need to remember the following laws of exponents rule: When multiplying variables, add the exponents.

$x^{5}\cdot x^{2}=x^{5+2}=x^{7}$

Combine these to get the final answer:

$6x^{7}$

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Question

Multiply the following monomial quotiemts:

$4x^{3}\cdot 7x$

Answer

To solve this problem, split it into two steps:

1. Multiply the coefficients

$4\cdot7=28$

2. Multiply the variables. We also need to remember the following laws of exponents rule: When multiplying variables, add the exponents.

$x^{3}\cdot x=x^{3+1}=x^{4}$

Combine these to get the final answer:

$28x^{4}$

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Question

Multiply the following monomial quotients:

$9x\cdot 6$

Answer

To solve this problem, split it into two steps:

1. Multiply the coefficients

$9\cdot6=54$

2. Combine this with the lone variable to get the final answer:

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Question

Multiply the following monomial quotients:

$8x^{2}\cdot 5x$

Answer

To solve this problem, split it into two steps:

1. Multiply the coefficients

$8\cdot5=40$

2. Multiply the variables. We also need to remember the following laws of exponents rule: When multiplying variables, add the exponents.

$x^{2}\cdot x=x^{2+1}=x^{3}$

Combine these to get the final answer:

$40x^{3}$

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Question

Multiply the following monomial quotients:

$6x\cdot 7x^{2}$

Answer

To solve this problem, split it into two steps:

1. Multiply the coefficients

$6\cdot7=42$

2. Multiply the variables. We also need to remember the following laws of exponents rule: When multiplying variables, add the exponents.

$x\cdot x^{2}=x^{1+2}=x^{3}$

Combine these to get the final answer:

$42x^{3}$

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Question

Multiply the following monomial quotients:

$3x^{5}\cdot 4x^{2}$

Answer

To solve this problem, split it into two steps:

1. Multiply the coefficients

$3\cdot4=12$

2. Multiply the variables. We also need to remember the following laws of exponents rule: When multiplying variables, add the exponents.

$x^{5}\cdot x^{2}=x^{5+2}=x^{7}$

Combine these to get the final answer:

$12x^{7}$

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Question

Multiply the following monomial quotients:

$9x\cdot 10$

Answer

To solve this problem, split it into two steps:

1. Multiply the coefficients

$9\cdot10=90$

2. Combine this with the lone variable e to get the final answer:

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Question

Multiply the following monomial quotients:

$12x^{2}\cdot 4x^{3}$

Answer

To solve this problem, split it into two steps:

1. Multiply the coefficients

$12\cdot4=48$

2. Multiply the variables. We also need to remember the following laws of exponents rule: When multiplying variables, add the exponents.

$x^{2}\cdot x^{3}=x^{2+3}=x^{5}$

Combine these to get the final answer:

$48x^{5}$

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Question

Multiply the following monomial quotients:

$5x\cdot 6x^{3}$

Answer

To solve this problem, split it into two steps:

1. Multiply the coefficients

$5\cdot6=30$

2. Multiply the variables. We also need to remember the following laws of exponents rule: When multiplying variables, add the exponents.

$x\cdot x^{3}=x^{1+3}=x^{4}$

Combine these to get the final answer:

$30x^{4}$

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Question

Choose the expression that is equal to $4z^{-6}z^{4}$ .

Answer

Remember that to multiply like variables with exponents you add the exponents.

This gives $4z^{-2}$ .

Also remember that a variable raised to a negative exponential is the same as 1/that same variable to that positive exponential.

For example, $z^{-2}$ is equivalent to $1/z^{2}$ .

This thinking leads to the answer $4/z^{2}$ .

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Question

Simplify the following:

$\frac{x}{y}\cdot\frac{y}{z}$

Answer

To solve, simply multiply numerators and denominators and then simplify. Thus,

$\frac{x}{y}\cdot\frac{y}{z}=\frac{xy}{yz}=\frac{x}{z}$

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Question

What is the degree of the following polynomial?

Answer

To find the degree of a polynomial, simply find the highest exponent in the expression. As two is the highest exponent above, it is also the degree of the polynomial.

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Question

Expand and simplify the expression:

$(2x+3y)^{-3}$

Answer

We are asked to expand and simplify the expression: $(2x+3y)^{-3}$ .

This question is going to require knowledge of exponent rules and FOIL methods.

The first step is to create an inverse reciprocal of a negative exponent.

$\frac{1}{(2x+3y)^{3}}$

Now, we can expand the expression by removing the exponent in the denominator.

$\frac{1}{(2x+3y)(2x+3y)(2x+3y)}$

Use the FOIL method to first multiply and .

You'll find it creates . Replace it back into the expression because we have to multiply the result by one more time.

$\frac{1}{(4x^2+12xy+9y^2)(2x+3y)}$

Be careful with exponents and coefficients!

$\frac{1}{8x^3+12{\color{DarkOrange} x^2y}+24{\color{DarkOrange} x^2y}+36{\color{Magenta} xy^2}+18{\color{Magenta} xy^2}+27y^3}$

Combine like terms to find the simplified answer.

$\frac{1}{8x^3+36x^2y+54xy^2+27y^3}$

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Question

What is the degree of the following polynomial?

Answer

To find the degree of a polynomial, simply find the highest exponent in the expression. As five is the highest exponent above, it is also the degree of the polynomial.

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