Select the equivalent expression. (x^(2))/(x^(-6)*x^(3)) (1)/(x) x^(5) (1)/(x^(5)) x

Simplify Expression: Simplify the expression using the properties of exponents. We have the expression (x^(2))/(x^(-6)*x^(3)). According to the properties of exponents, when we divide powers with the same base, we subtract the exponents. When we multiply powers with the same base, we add the exponents.Apply Properties of Exponents: Apply the properties of exponents to the denominator. First, we combine the exponents in the denominator by adding them because they have the same base and are being multiplied. x^(-6) * x^(3) = x^(-6 + 3) = x^(-3)Divide Powers: Divide the powers with the same base. Now we divide x^(2) by x^(-3). According to the properties of exponents, we subtract the exponent in the denominator from the exponent in the numerator. x^(2) / x^(-3) = x^(2 - (-3)) = x^(2 + 3) = x^(5)

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Select the equivalent expression.

(x^(2))/(x^(-6)*x^(3))

(1)/(x)

x^(5)

(1)/(x^(5))

x

Select the equivalent expression. $\newline$ $\frac{x^{2}}{x^{-6} \cdot x^{3}}$ $\newline$ $\frac{1}{x}$ $\newline$ $x^{5}$ $\newline$ $\frac{1}{x^{5}}$ $\newline$ $x$

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Math Problems

Algebra 1

Multiplication with rational exponents

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Q. Select the equivalent expression.

\newline

\frac{x^{2}}{x^{-6} \cdot x^{3}}

\newline

\frac{1}{x}

\newline

x^{5}

\newline

\frac{1}{x^{5}}

\newline

x

Simplify Expression: Simplify the expression using the properties of exponents. $\newline$ We have the expression $(x^{2})/(x^{-6}*x^{3})$ . According to the properties of exponents, when we divide powers with the same base, we subtract the exponents. When we multiply powers with the same base, we add the exponents.
Apply Properties of Exponents: Apply the properties of exponents to the denominator. $\newline$ First, we combine the exponents in the denominator by adding them because they have the same base and are being multiplied. $\newline$ $x^{-6} \times x^{3} = x^{-6 + 3} = x^{-3}$
Divide Powers: Divide the powers with the same base. $\newline$ Now we divide $x^{2}$ by $x^{-3}$ . According to the properties of exponents, we subtract the exponent in the denominator from the exponent in the numerator. $\newline$ $x^{2} / x^{-3} = x^{2 - (-3)} = x^{2 + 3} = x^{5}$