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Which expression is equivalent to
((15)/(8))^(0)*((2)/(5))^(-3) ?
0
1

((5)/(2))^(3)

((30)/(40))^(-3)

Which expression is equivalent to $\left(\frac{15}{8}\right)^{0} \cdot\left(\frac{2}{5}\right)^{-3}$ ? $\newline$ $0$ $\newline$ $1$ $\newline$ $\left(\frac{5}{2}\right)^{3}$ $\newline$ $\left(\frac{30}{40}\right)^{-3}$

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Multiplication with rational exponents

Full solution

Q. Which expression is equivalent to

\left(\frac{15}{8}\right)^{0} \cdot\left(\frac{2}{5}\right)^{-3}

?

\newline

0

\newline

1

\newline

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

\newline

\left(\frac{30}{40}\right)^{-3}

Simplify to $1$ : First, simplify $\left(\frac{15}{8}\right)^0$ . Any number raised to the power of $0$ is $1$ . $\newline$ $\left(\frac{15}{8}\right)^0 = 1$
Negative Exponent Rule: Next, simplify $\left(\frac{2}{5}\right)^{-3}$ . A negative exponent means we take the reciprocal and then raise it to the positive exponent. $\newline$ $\left(\frac{2}{5}\right)^{-3} = \left(\frac{5}{2}\right)^3$
Multiply Results: Now, multiply the results from the previous steps. $\newline$ $1 \cdot \left(\frac{5}{2}\right)^3 = \left(\frac{5}{2}\right)^3$

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