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

Answer 1

Answer: A

Explanation:

-9•9•9= -729a 9/3= 3

6/3=b^ 2

Answer 2

`\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`