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Simplify:

(-9d^(5))^(3)
Answer:

Simplify: $\newline$ $\left(-9 d^{5}\right)^{3}$ $\newline$ Answer:

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Evaluate rational exponents

Full solution

Q. Simplify:

\newline

\left(-9 d^{5}\right)^{3}

\newline

Answer:

Identify base and exponent: Identify the base and the exponent in $(-9d^{5})^{3}$ . $\newline$ In $(-9d^{5})^{3}$ , $\newline$ Base: $-9d^{5}$ $\newline$ Exponent: $3$
Apply power of power rule: Apply the power of a power rule, which states that $(a^m)^n = a^{m*n}$ . $\newline$ $(-9d^{5})^{3} = (-9)^3 \times (d^{5})^3$
Calculate cube of $-9$ : Calculate the cube of $-9$ . $(-9)^3 = -9 \times -9 \times -9$ $= -729$
Apply power of power rule to $d^{5}$ : Apply the power of a power rule to $d^{5}$ .
$(d^{5})^{3} = d^{5*3}$
$= d^{15}$
Combine results: Combine the results from Step $3$ and Step $4$ . $\newline$ $(-9d^{5})^{3} = -729 \times d^{15}$

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