What is the cube root of -729a^9b^6? A. -9a^3b^2 B. -9a^2b^3 C. -8a^3b^2 D. -8a^2b^3

Question

What is the cube root of -729a^9b^6?

A. -9a^3b^2
B. -9a^2b^3
C. -8a^3b^2
D. -8a^2b^3

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Gianna 2 weeks 2021-09-10T23:55:26+00:00 2 Answers 0

Answers ( )

    0
    2021-09-10T23:56:39+00:00

    Answer:

    \large\boxed{A.\ -9a^3b^2}

    Step-by-step explanation:

    \sqrt[3]{-729a^9b^6}\qquad\text{use}\ \sqrt[n]{xy}=\sqrt[n]{x}\cdot\sqrt[n]{y}\\\\=\sqrt[3]{-729}\cdot\sqrt[3]{a^9}\cdot\sqrt[3]{b^6}\\\\=-9\cdot\sqrt[3]{a^{(3)(3)}}\cdot\sqrt[3]{b^{(2)(3)}}\qquad\text{use}\ (x^n)^m=x^{nm}\\\\=-9\cdot\sqrt[3]{(a^3)^3}\cdot\sqrt[3]{(b^2)^3}\qquad\text{use}\ \sqrt[3]{x^3}=x\\\\=-9a^3b^2

    0
    2021-09-10T23:56:43+00:00

    Answer: A

    Step-by-step explanation:

    -9•9•9= -729a 9/3= 3

    6/3=b^ 2

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