Question

HALLPPP its worth 50 points

Answer 1

Rewrite the innermost expressions with negative exponents:

$\displaystyle \left[\left(\frac{a^6}{5b^{-1}}\right)^2 \cdot \left(\frac{b}{9a^{-11}}\right)^{-1}\right]^{-3}$

$\displaystyle \implies \left[\left(\frac{a^6b^1}{5}\right)^2 \cdot \left(\frac{ba^{11}}{9}\right)^{-1}\right]^{-3}$

$\displaystyle \implies \left[\left(\frac{a^6b^1}{5}\right)^2 \cdot \left(\frac9{ba^{11}}\right)^1\right]^{-3}$

Simplify the product:

$\displaystyle \implies \left[\left(\frac{a^6b}{5}\right)^2 \cdot \frac9{ba^{11}}\right]^{-3}$

$\displaystyle \implies \left[\frac{\left(a^6b\right)^2}{5^2} \cdot \frac9{ba^{11}}\right]^{-3}$

$\displaystyle \implies \left[\frac{\left(a^6\right)^2b^2}{25} \cdot \frac9{ba^{11}}\right]^{-3}$

$\displaystyle \implies \left[\frac{a^{12}b^2}{25} \cdot \frac9{ba^{11}}\right]^{-3}$

$\displaystyle \implies \left[\frac{9ab}{25}\right]^{-3}$

Rewrite the last negative exponent:

$\implies \boxed{\left(\frac{25}{9ab}\right)^3}$