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3 votes
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

2 Answers

6 votes

Answer: A

Explanation:

-9•9•9= -729a 9/3= 3

6/3=b^ 2

User Abevieiramota
by
6.9k points
4 votes

Answer:


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

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

User VARAK
by
7.6k points