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$Simplify. ((2)/(5))^(3)= (Type a simplified fraction.)$

Simplify. $\newline$ $\left(\frac{2}{5}\right)^{3}=$ $\newline$ (Type a simplified fraction.)

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Evaluate rational exponents

Full solution

Q. Simplify.

\newline

\left(\frac{2}{5}\right)^{3}=

\newline

(Type a simplified fraction.)

Identify base and exponent: Identify the base and the exponent in $\left(\frac{2}{5}\right)^3$ . In $\left(\frac{2}{5}\right)^3$ , the base is $\left(\frac{2}{5}\right)$ and the exponent is $3$ .
Apply exponent to fraction: Apply the exponent to both the numerator and the denominator. $\newline$ When raising a fraction to a power, you raise both the numerator and the denominator to that power. $\newline$ $\left(\frac{2}{5}\right)^3 = \frac{2^3}{5^3}$
Calculate powers: Calculate the powers of the numerator and the denominator. $\newline$ $2^3 = 2 \times 2 \times 2 = 8$ $\newline$ $5^3 = 5 \times 5 \times 5 = 125$
Write simplified fraction: Write the result as a simplified fraction. $\newline$ The fraction becomes $(8)/(125)$ .

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