Select the equivalent expression. (x^(8))/(x^(-1)*x^(-5)) (1)/(x^(4)) x^(14) x^(4) (1)/(x^(14))

Simplify Exponents: Simplify the denominator using the property of exponents that states when you multiply powers with the same base, you add the exponents. x^(-1) * x^(-5) = x^(-1 + -5) = x^(-6)Rewrite Expression: Rewrite the original expression with the simplified denominator. (x^(8))/(x^(-1)*x^(-5)) becomes (x^(8))/(x^(-6))Apply Exponent Rule: Use the property of exponents that states when you divide powers with the same base, you subtract the exponents. (x^(8))/(x^(-6)) = x^(8 - (-6)) = x^(8 + 6) = x^(14)

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Select the equivalent expression.

(x^(8))/(x^(-1)*x^(-5))

(1)/(x^(4))

x^(14)

x^(4)

(1)/(x^(14))

Select the equivalent expression. $\newline$ $\frac{x^{8}}{x^{-1} \cdot x^{-5}}$ $\newline$ $\frac{1}{x^{4}}$ $\newline$ $x^{14}$ $\newline$ $x^{4}$ $\newline$ $\frac{1}{x^{14}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\frac{x^{8}}{x^{-1} \cdot x^{-5}}

\newline

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

\newline

x^{14}

\newline

x^{4}

\newline

\frac{1}{x^{14}}

Simplify Exponents: Simplify the denominator using the property of exponents that states when you multiply powers with the same base, you add the exponents. $\newline$ $x^{-1} \times x^{-5} = x^{-1 + -5}$ $\newline$ $= x^{-6}$
Rewrite Expression: Rewrite the original expression with the simplified denominator. $\newline$ $(x^{8})/(x^{-1}*x^{-5})$ becomes $(x^{8})/(x^{-6})$
Apply Exponent Rule: Use the property of exponents that states when you divide powers with the same base, you subtract the exponents. $\newline$ $(x^{8})/(x^{-6}) = x^{8 - (-6)}$ $\newline$ = $x^{8 + 6}$ $\newline$ = $x^{14}$