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

Simplify Exponents: Simplify the expression by dividing the exponents. When dividing powers with the same base, subtract the exponents. (x^(-6)y^(-1))/(xy^(5)) = x^(-6-1)y^(-1-5)Subtract Exponents: Perform the subtraction of exponents. x^(-6-1) = x^(-7) y^(-1-5) = y^(-6) So, the expression becomes x^(-7)y^(-6).Convert Negative Exponents: Rewrite the expression with positive exponents. To convert a negative exponent to a positive exponent, take the reciprocal of the base. x^(-7)y^(-6) = (1/x^7)(1/y^6) = 1/(x^7y^6)Match Simplified Expression: Match the simplified expression with the given options. The simplified expression is 1/(x^7y^6), which matches the option (1)/(x^(7)y^(6)).

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Select the equivalent expression.

(x^(-6)y^(-1))/(xy^(5))

x^(7)

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

(1)/(x^(7))

x^(7)y^(6)

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

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\frac{x^{-6} y^{-1}}{x y^{5}}

\newline

x^{7}

\newline

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

\newline

\frac{1}{x^{7}}

\newline

x^{7} y^{6}

Simplify Exponents: Simplify the expression by dividing the exponents. $\newline$ When dividing powers with the same base, subtract the exponents. $\newline$ $\frac{x^{(-6)}y^{(-1)}}{xy^{(5)}} = x^{(-6-1)}y^{(-1-5)}$
Subtract Exponents: Perform the subtraction of exponents. $x^{(-6-1)} = x^{-7}$ $y^{(-1-5)} = y^{-6}$ So, the expression becomes $x^{-7}y^{-6}$ .
Convert Negative Exponents: Rewrite the expression with positive exponents. $\newline$ To convert a negative exponent to a positive exponent, take the reciprocal of the base. $\newline$ $x^{-7}y^{-6} = (1/x^7)(1/y^6) = 1/(x^7y^6)$
Match Simplified Expression: Match the simplified expression with the given options. $\newline$ The simplified expression is $\frac{1}{x^7y^6}$ , which matches the option $\frac{1}{x^{7}y^{6}}$ .