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Algebra II : Multiplying and Dividing Exponents

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Example Questions

Example Question #171 : Multiplying And Dividing Exponents

Simplify $x^2y^3x^{-3}y^7$ $\displaystyle x^2y^3x^{-3}y^7$

Possible Answers:

x^2y^7 $\displaystyle x^2y^7$

Not possible.

$x^7y^{2}$ $\displaystyle x^7y^{2}$

$\frac{y^{10}}{x}$ $\displaystyle \frac{y^{10}}{x}$

$\frac{x^2y^{10}}{x^3}$ $\displaystyle \frac{x^2y^{10}}{x^3}$

Correct answer:

$\frac{y^{10}}{x}$ $\displaystyle \frac{y^{10}}{x}$

Explanation:

First combine like variables. This leaves us with $x^{-1}y^{10}$ $\displaystyle x^{-1}y^{10}$ which is equal to $\frac{y^{10}}{x}$ $\displaystyle \frac{y^{10}}{x}$

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Example Question #172 : Multiplying And Dividing Exponents

Simplify $\displaystyle x^2y^4z^5x^5z^7y^8$

Possible Answers:

$(xyz)^{31}$ $\displaystyle (xyz)^{31}$

$1/x^7y^{12}z^{12}$ $\displaystyle 1/x^7y^{12}z^{12}$

$x^7y^{12}z^{12}$ $\displaystyle x^7y^{12}z^{12}$

Not possible.

Correct answer:

$x^7y^{12}z^{12}$ $\displaystyle x^7y^{12}z^{12}$

Explanation:

First combine like variables by adding exponents. This leaves us with $x^7y^{12}z^{12}$ $\displaystyle x^7y^{12}z^{12}$

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Example Question #173 : Multiplying And Dividing Exponents

Simplify $\frac{x^7y^2z^8x^2y^{16}}{x^9y^{18}}$ $\displaystyle \frac{x^7y^2z^8x^2y^{16}}{x^9y^{18}}$

Possible Answers:

z^8 $\displaystyle z^8$

xyz^8 $\displaystyle xyz^8$

Not possible

$x^{18}y^{36}z^8$ $\displaystyle x^{18}y^{36}z^8$

Correct answer:

z^8 $\displaystyle z^8$

Explanation:

First, combine exponents of like variables. This gives us $\frac{x^9y^{18}z^8}{x^9y^{18}}$ $\displaystyle \frac{x^9y^{18}z^8}{x^9y^{18}}$ which simplifies to z^8 $\displaystyle z^8$

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Example Question #174 : Multiplying And Dividing Exponents

Simplify $x^5y^2x^{-4}$ $\displaystyle x^5y^2x^{-4}$

Possible Answers:

$\frac{x}{y^2}$ $\displaystyle \frac{x}{y^2}$

$\displaystyle 0$

x^2y $\displaystyle x^2y$

(xy)^2 $\displaystyle (xy)^2$

xy^2 $\displaystyle xy^2$

Correct answer:

xy^2 $\displaystyle xy^2$

Explanation:

First, combine exponents of like variables. This gives us xy^2 $\displaystyle xy^2$

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Example Question #175 : Multiplying And Dividing Exponents

Simplify $z^3y^2x^6y^{-3}$ $\displaystyle z^3y^2x^6y^{-3}$

Possible Answers:

$\displaystyle z^3y^2x^6$

(xyz)^8 $\displaystyle (xyz)^8$

$\frac{z^3x^6}{y}$ $\displaystyle \frac{z^3x^6}{y}$

$\frac{z^3x^6}{y^3}$ $\displaystyle \frac{z^3x^6}{y^3}$

Correct answer:

$\frac{z^3x^6}{y}$ $\displaystyle \frac{z^3x^6}{y}$

Explanation:

First, combine exponents of like variables. This gives us $z^3y^{-1}x^6$ $\displaystyle z^3y^{-1}x^6$ which simplifies to $\frac{z^3x^6}{y}$ $\displaystyle \frac{z^3x^6}{y}$

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Example Question #176 : Multiplying And Dividing Exponents

Simplify $x^8z^2y^3x^4y^{18}z^2z^{-14}y^{-23}y^{12}x^{-3}z^{22}x^{-9}$ $\displaystyle x^8z^2y^3x^4y^{18}z^2z^{-14}y^{-23}y^{12}x^{-3}z^{22}x^{-9}$

Possible Answers:

y^3 $\displaystyle y^3$

$\displaystyle 1$

$y^{10}z^{12}$ $\displaystyle y^{10}z^{12}$

x^2 $\displaystyle x^2$

$x^{24}y^{45}z^{25}$ $\displaystyle x^{24}y^{45}z^{25}$

Correct answer:

$y^{10}z^{12}$ $\displaystyle y^{10}z^{12}$

Explanation:

First, combine exponents of like variables and add them together. This gives us $x^0y^{10}z^{12}$ $\displaystyle x^0y^{10}z^{12}$ which simplifies to $y^{10}z^{12}$ $\displaystyle y^{10}z^{12}$

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Example Question #177 : Multiplying And Dividing Exponents

The expression $\frac{a^{3}b^{-2}}{a^{-4}b^{2}}$ $\displaystyle \frac{a^{3}b^{-2}}{a^{-4}b^{2}}$ is equivalent to?

Possible Answers:

$\frac{a^{7}}{b^{4}}$ $\displaystyle \frac{a^{7}}{b^{4}}$

$\frac{a^{3}}{b^{2}}$ $\displaystyle \frac{a^{3}}{b^{2}}$

$\frac{b^{5}}{a^{7}}$ $\displaystyle \frac{b^{5}}{a^{7}}$

$\displaystyle 1$

$a^{-2}b^{-2}$ $\displaystyle a^{-2}b^{-2}$

Correct answer:

$\frac{a^{7}}{b^{4}}$ $\displaystyle \frac{a^{7}}{b^{4}}$

Explanation:

By simplifying the exponents: bringing the $a^{-4}$ $\displaystyle a^{-4}$ to the numerator and adding the two a's together, getting $a^{7}$ $\displaystyle a^{7}$ in the numerator, and bringing the $b^{-2}$ $\displaystyle b^{-2}$ to the denominator and adding the two b's together, getting $b^{4}$ $\displaystyle b^{4}$ in the denominator.

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Example Question #178 : Multiplying And Dividing Exponents

Divide the exponents: $\frac{2^{8}}{2^{10}}$ $\displaystyle \frac{2^{8}}{2^{10}}$

Possible Answers:

$\frac{1}{4}$ $\displaystyle \frac{1}{4}$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\frac{1}{256}$ $\displaystyle \frac{1}{256}$

$-\frac{1}{4}$ $\displaystyle -\frac{1}{4}$

$\frac{1}{512}$ $\displaystyle \frac{1}{512}$

Correct answer:

$\frac{1}{4}$ $\displaystyle \frac{1}{4}$

Explanation:

Since both of the terms are divided and share a common base, we can simplify the exponents by subtraction.

$\frac{2^{8}}{2^{10}} = 2^{8-10} = 2^{-2}$ $\displaystyle \frac{2^{8}}{2^{10}} = 2^{8-10} = 2^{-2}$

The negative exponent can be rewritten as fraction.

$2^{-2} = \frac{1}{2^2} = \frac{1}{4}$ $\displaystyle 2^{-2} = \frac{1}{2^2} = \frac{1}{4}$

The answer is: $\frac{1}{4}$ $\displaystyle \frac{1}{4}$

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Example Question #179 : Multiplying And Dividing Exponents

Simplify: $\frac{x^{-5}}{x^{-6}} \div x^{-5}$ $\displaystyle \frac{x^{-5}}{x^{-6}} \div x^{-5}$

Possible Answers:

$\frac{1}{x^6}$ $\displaystyle \frac{1}{x^6}$

$\frac{1}{x^4}$ $\displaystyle \frac{1}{x^4}$

$\frac{1}{x^2}$ $\displaystyle \frac{1}{x^2}$

$\frac{1}{x^{16}}$ $\displaystyle \frac{1}{x^{16}}$

x^6 $\displaystyle x^6$

Correct answer:

x^6 $\displaystyle x^6$

Explanation:

Evaluate the first term by subtracting the exponents.

$\frac{x^{-5}}{x^{-6}} = x^{-5-(-6)} = x^{-5+6} = x^1=x$ $\displaystyle \frac{x^{-5}}{x^{-6}} = x^{-5-(-6)} = x^{-5+6} = x^1=x$

$x\div x^{-5} = \frac{x^1}{x^{-5}} = x^{1-(-5)} = x^6$ $\displaystyle x\div x^{-5} = \frac{x^1}{x^{-5}} = x^{1-(-5)} = x^6$

The answer is: x^6 $\displaystyle x^6$

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Example Question #180 : Multiplying And Dividing Exponents

Solve: $\frac{2^8}{4^{5}}$ $\displaystyle \frac{2^8}{4^{5}}$

Possible Answers:

$\frac{1}{32}$ $\displaystyle \frac{1}{32}$

$\frac{1}{8}$ $\displaystyle \frac{1}{8}$

$\frac{1}{4}$ $\displaystyle \frac{1}{4}$

$\frac{1}{16}$ $\displaystyle \frac{1}{16}$

$\frac{1}{4096}$ $\displaystyle \frac{1}{4096}$

Correct answer:

$\frac{1}{4}$ $\displaystyle \frac{1}{4}$

Explanation:

Do not expand the powers. Instead convert the denominator to base two.

$\frac{2^8}{4^{5}} = \frac{2^8}{(2^2)^{5}} = \frac{2^8}{2^{10}}$ $\displaystyle \frac{2^8}{4^{5}} = \frac{2^8}{(2^2)^{5}} = \frac{2^8}{2^{10}}$

Now that common bases with a certain exponent are divided, we can subtract the exponents.

$2^{8-10} = 2^{-2}$ $\displaystyle 2^{8-10} = 2^{-2}$

Rewrite this term as a fraction.

$2^{-2} = \frac{1}{2^2} = \frac{1}{4}$ $\displaystyle 2^{-2} = \frac{1}{2^2} = \frac{1}{4}$

The answer is: $\frac{1}{4}$ $\displaystyle \frac{1}{4}$

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Algebra II : Multiplying and Dividing Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #171 : Multiplying And Dividing Exponents

Example Question #172 : Multiplying And Dividing Exponents

Example Question #173 : Multiplying And Dividing Exponents

Example Question #174 : Multiplying And Dividing Exponents

Example Question #175 : Multiplying And Dividing Exponents

Example Question #176 : Multiplying And Dividing Exponents

Example Question #177 : Multiplying And Dividing Exponents

Example Question #178 : Multiplying And Dividing Exponents

Example Question #179 : Multiplying And Dividing Exponents

Example Question #180 : Multiplying And Dividing Exponents

All Algebra II Resources

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