Select the equivalent expression. (x^(8)y^(2))/(x^(7)y^(-7)) xy^(9) (x)/(y^(5)) (y^(5))/(x) (1)/(xy^(9))

Divide and Subtract Exponents: Simplify the expression by dividing the powers with the same base. When dividing powers with the same base, subtract the exponents. (x^(8)y^(2))/(x^(7)y^(-7)) = x^(8-7)y^(2-(-7))Perform Subtraction: Perform the subtraction of the exponents. x^(8-7) = x^(1) = x y^(2-(-7)) = y^(2+7) = y^(9) So, the simplified expression is x * y^(9).Check Options: Check the given options to see which one matches the simplified expression. The simplified expression is x * y^(9), which matches the first option: xy^(9).

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Select the equivalent expression.

(x^(8)y^(2))/(x^(7)y^(-7))

xy^(9)

(x)/(y^(5))

(y^(5))/(x)

(1)/(xy^(9))

Select the equivalent expression. $\newline$ $\frac{x^{8} y^{2}}{x^{7} y^{-7}}$ $\newline$ $x y^{9}$ $\newline$ $\frac{x}{y^{5}}$ $\newline$ $\frac{y^{5}}{x}$ $\newline$ $\frac{1}{x y^{9}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\frac{x^{8} y^{2}}{x^{7} y^{-7}}

\newline

x y^{9}

\newline

\frac{x}{y^{5}}

\newline

\frac{y^{5}}{x}

\newline

\frac{1}{x y^{9}}

Divide and Subtract Exponents: Simplify the expression by dividing the powers with the same base. $\newline$ When dividing powers with the same base, subtract the exponents. $\newline$ $\frac{x^{8}y^{2}}{x^{7}y^{-7}} = x^{8-7}y^{2-(-7)}$
Perform Subtraction: Perform the subtraction of the exponents. $\newline$ $x^{(8-7)} = x^{1} = x$ $\newline$ $y^{(2-(-7))} = y^{(2+7)} = y^{9}$ $\newline$ So, the simplified expression is $x \cdot y^{9}$ .
Check Options: Check the given options to see which one matches the simplified expression. $\newline$ The simplified expression is $x * y^{9}$ , which matches the first option: $xy^{9}$ .