Select the equivalent expression. (x^(2))/(x^(-1)*x^(7)) (1)/(x^(6)) x^(6) x^(4) (1)/(x^(4))

Simplify Denominator: Simplify the denominator using the properties of exponents. When multiplying powers with the same base, you add the exponents. x^(-1) * x^(7) = x^(-1 + 7)Calculate Exponent Sum: Calculate the sum of the exponents in the denominator. -1 + 7 = 6 So, x^(-1) * x^(7) = x^(6)Rewrite Expression: Rewrite the original expression with the simplified denominator. (x^(2))/(x^(-1)*x^(7)) becomes (x^(2))/(x^(6))Simplify Using Exponents: Simplify the expression using the properties of exponents. When dividing powers with the same base, you subtract the exponents. (x^(2))/(x^(6)) = x^(2-6)Calculate Exponent Difference: Calculate the difference of the exponents. 2 - 6 = -4 So, (x^(2))/(x^(6)) = x^(-4)Recognize Equivalent Expression: Recognize that x^(-4) is the same as 1/(x^(4)). Therefore, the equivalent expression is (1)/(x^(4)).

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Select the equivalent expression.

(x^(2))/(x^(-1)*x^(7))

(1)/(x^(6))

x^(6)

x^(4)

(1)/(x^(4))

Select the equivalent expression. $\newline$ $\frac{x^{2}}{x^{-1} \cdot x^{7}}$ $\newline$ $\frac{1}{x^{6}}$ $\newline$ $x^{6}$ $\newline$ $x^{4}$ $\newline$ $\frac{1}{x^{4}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\frac{x^{2}}{x^{-1} \cdot x^{7}}

\newline

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

\newline

x^{6}

\newline

x^{4}

\newline

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

Simplify Denominator: Simplify the denominator using the properties of exponents. $\newline$ When multiplying powers with the same base, you add the exponents. $\newline$ $x^{-1} \times x^{7} = x^{-1 + 7}$
Calculate Exponent Sum: Calculate the sum of the exponents in the denominator. $\newline$ $-1 + 7 = 6$ $\newline$ So, $x^{-1} \times x^{7} = x^{6}$
Rewrite Expression: Rewrite the original expression with the simplified denominator. $\newline$ $(x^{2})/(x^{-1}*x^{7})$ becomes $(x^{2})/(x^{6})$
Simplify Using Exponents: Simplify the expression using the properties of exponents. $\newline$ When dividing powers with the same base, you subtract the exponents. $\newline$ $\frac{x^{2}}{x^{6}} = x^{2-6}$
Calculate Exponent Difference: Calculate the difference of the exponents. $\newline$ $2 - 6 = -4$ $\newline$ So, $(x^{2})/(x^{6}) = x^{-4}$
Recognize Equivalent Expression: Recognize that $x^{-4}$ is the same as $\frac{1}{x^{4}}$ . Therefore, the equivalent expression is $\frac{1}{x^{4}}$ .