Question

Simplify the expression:
6sqrt64a^9
(6 squareroot of 64a^9 )
Please help!!!!

Answer 1

\(\bf 6\sqrt{64a^9}\qquad 64\implies 8^2\qquad a^9\implies a^4\cdot a^4\cdot a\implies (a^4)^2\cdot a\\ \quad \\

6\sqrt{64a^9}\implies \Large 6\sqrt[{\color{red}{ 2}}]{8^{\color{red}{ 2}}(a^4)^{\color{red}{ 2}}\cdot a}\)

Answer 2

I appreciate your trying to be really clear regarding the expression you want to simplify.

Order of operations rules apply here. Your sqrt(64a^9) is equivalent to
\[(64a ^{9})^{1/2}\],

Answer 3

so you must do the exponentiation BEFORE the multiplication by 6.

Sqrt (64) = 8; Sqrt (a^9) = a^(9/2).

Thus, your math problem boils down to

6*8*a^(9/2).