Select the equivalent expression. (x^(-1)x^(-6)y^(7))/(y^(2)) (y^(5))/(x^(7)) (x^(5))/(y^(5)) (x^(7))/(y^(5)) (y^(5))/(x^(5))

Combine powers of x: Simplify the expression by combining the powers of x. When multiplying powers with the same base, you add the exponents. (x^(-1) * x^(-6)) * y^(7) / y^(2) = x^(-1 + -6) * y^(7) / y^(2) = x^(-7) * y^(7) / y^(2)Combine powers of y: Simplify the expression by combining the powers of y. When dividing powers with the same base, you subtract the exponents. x^(-7) * (y^(7) / y^(2)) = x^(-7) * y^(7 - 2) = x^(-7) * y^(5)Rewrite with positive exponents: Rewrite the expression with positive exponents. x^(-7) can be written as 1/x^(7). So, x^(-7) * y^(5) becomes (y^(5)) / (x^(7))

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Select the equivalent expression.

(x^(-1)x^(-6)y^(7))/(y^(2))

(y^(5))/(x^(7))

(x^(5))/(y^(5))

(x^(7))/(y^(5))

(y^(5))/(x^(5))

Select the equivalent expression. $\newline$ $\frac{x^{-1} x^{-6} y^{7}}{y^{2}}$ $\newline$ $\frac{y^{5}}{x^{7}}$ $\newline$ $\frac{x^{5}}{y^{5}}$ $\newline$ $\frac{x^{7}}{y^{5}}$ $\newline$ $\frac{y^{5}}{x^{5}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\frac{x^{-1} x^{-6} y^{7}}{y^{2}}

\newline

\frac{y^{5}}{x^{7}}

\newline

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

\newline

\frac{x^{7}}{y^{5}}

\newline

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

Combine powers of x: Simplify the expression by combining the powers of x. $\newline$ When multiplying powers with the same base, you add the exponents. $\newline$ $(x^{-1} \cdot x^{-6}) \cdot y^{7} / y^{2}$ $\newline$ = $x^{-1 + -6} \cdot y^{7} / y^{2}$ $\newline$ = $x^{-7} \cdot y^{7} / y^{2}$
Combine powers of y: Simplify the expression by combining the powers of y. $\newline$ When dividing powers with the same base, you subtract the exponents. $\newline$ $x^{-7} \cdot \left(\frac{y^{7}}{y^{2}}\right)$ $\newline$ = $x^{-7} \cdot y^{7 - 2}$ $\newline$ = $x^{-7} \cdot y^{5}$
Rewrite with positive exponents: Rewrite the expression with positive exponents. $\newline$ $x^{-7}$ can be written as $\frac{1}{x^{7}}$ . $\newline$ So, $x^{-7} \cdot y^{5}$ becomes $\frac{y^{5}}{x^{7}}$