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

Simplify numerator: Simplify the numerator by adding exponents. When multiplying powers with the same base, you add the exponents. (x*x^(3)) = x^(1+3) = x^(4)Divide powers: Divide the powers by subtracting exponents. When dividing powers with the same base, you subtract the exponents. (x^(4))/(x^(5)) = x^(4-5) = x^(-1)Rewrite negative exponent: Rewrite the negative exponent as a positive exponent in the denominator. A negative exponent means that the base is on the wrong side of the fraction line, so you flip it to the other side to make the exponent positive. x^(-1) = 1/(x^(1)) = 1/x

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Select the equivalent expression.

(x*x^(3))/(x^(5))

(1)/(x^(3))

(1)/(x)

x

x^(3)

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

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\frac{x \cdot x^{3}}{x^{5}}

\newline

\frac{1}{x^{3}}

\newline

\frac{1}{x}

\newline

x

\newline

x^{3}

Simplify numerator: Simplify the numerator by adding exponents. $\newline$ When multiplying powers with the same base, you add the exponents. $\newline$ $x\times x^{3}$ = $x^{1+3}$ = $x^{4}$
Divide powers: Divide the powers by subtracting exponents. $\newline$ When dividing powers with the same base, you subtract the exponents. $\newline$ $\frac{x^{4}}{x^{5}} = x^{4-5} = x^{-1}$
Rewrite negative exponent: Rewrite the negative exponent as a positive exponent in the denominator. $\newline$ A negative exponent means that the base is on the wrong side of the fraction line, so you flip it to the other side to make the exponent positive. $\newline$ $x^{-1} = \frac{1}{x^{1}} = \frac{1}{x}$