Question

Which expression is equivalent to 4√144a^12b^3? PLEASE answer thank you!

Answer 1

The answer is 2a^3(4√9b^3)

Also known as A

Answer 2

Answer:$2a^3\sqrt[4]{9b^3}$ is equivalent to $\sqrt[4]{144a^{12}b^3}$.

Explanation: Since, given expression, $\sqrt[4]{144a^{12}b^3}$

Since, we can write,

$\sqrt[4]{144a^{12}b^3}=\sqrt[4]{16\times9\times (a^3)^4 b^3}$     (because, a^{mn}=(a^n)^m

⇒$\sqrt[4]{144a^{12}b^3}=\sqrt[4]{(2)^4\times9\times (a^3)^4\times b^3}$

⇒$\sqrt[4]{144a^{12}b^3}=2a^3\sqrt[4]{9 \times b^3}$