Select the equivalent expression. (x^(-3))/(x^(3)*x^(-7)) x^(7) (1)/(x) (1)/(x^(7)) x

Simplify using properties of exponents: Simplify the expression using the properties of exponents. When dividing powers with the same base, subtract the exponents. (x^(-3))/(x^(3)*x^(-7)) = x^(-3)/(x^(3-7))Perform subtraction in exponent: Continue simplifying the expression by performing the subtraction in the exponent. x^(-3)/(x^(3-7)) = x^(-3)/(x^(-4))Further simplify using properties: Simplify the expression further using the properties of exponents. When dividing powers with the same base, subtract the exponents. x^(-3)/(x^(-4)) = x^(-3 - (-4)) = x^(-3 + 4) = x^(1)Check for final simplification: Check the final expression for any possible simplification. x^(1) is already in its simplest form, as any number raised to the power of 1 is the number itself.

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Select the equivalent expression.

(x^(-3))/(x^(3)*x^(-7))

x^(7)

(1)/(x)

(1)/(x^(7))

x

Select the equivalent expression. $\newline$ $\frac{x^{-3}}{x^{3} \cdot x^{-7}}$ $\newline$ $x^{7}$ $\newline$ $\frac{1}{x}$ $\newline$ $\frac{1}{x^{7}}$ $\newline$ $x$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\frac{x^{-3}}{x^{3} \cdot x^{-7}}

\newline

x^{7}

\newline

\frac{1}{x}

\newline

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

\newline

x

Simplify using properties of exponents: Simplify the expression using the properties of exponents. $\newline$ When dividing powers with the same base, subtract the exponents. $\newline$ $\frac{x^{-3}}{x^{3}\cdot x^{-7}} = x^{-3}/x^{3-7}$
Perform subtraction in exponent: Continue simplifying the expression by performing the subtraction in the exponent. $x^{-3}/(x^{3-7}) = x^{-3}/(x^{-4})$
Further simplify using properties: Simplify the expression further using the properties of exponents. $\newline$ When dividing powers with the same base, subtract the exponents. $\newline$ $x^{-3}/(x^{-4}) = x^{-3 - (-4)} = x^{-3 + 4} = x^{1}$
Check for final simplification: Check the final expression for any possible simplification. $x^{(1)}$ is already in its simplest form, as any number raised to the power of $1$ is the number itself.