Question

simplify. assume all variables are positive.
(16xy)^{-\frac{3}{4}}
write your answer in the form a or \frac{a}{b}, where a and b are constants or variable expressions that have no variables in common. all exponents in your answer should be positive.

Explanation:

Step1: Apply power - of - product rule

$(16xy)^{-\frac{3}{4}}=16^{-\frac{3}{4}}x^{-\frac{3}{4}}y^{-\frac{3}{4}}$

Step2: Rewrite negative exponents as positive exponents

$16^{-\frac{3}{4}}x^{-\frac{3}{4}}y^{-\frac{3}{4}}=\frac{1}{16^{\frac{3}{4}}x^{\frac{3}{4}}y^{\frac{3}{4}}}$

Step3: Simplify $16^{\frac{3}{4}}$

$16^{\frac{3}{4}}=(16^{\frac{1}{4}})^3$. Since $16^{\frac{1}{4}} = 2$ (because $2^4=16$), then $(16^{\frac{1}{4}})^3=2^3 = 8$.

Step4: Get the final simplified form

$\frac{1}{16^{\frac{3}{4}}x^{\frac{3}{4}}y^{\frac{3}{4}}}=\frac{1}{8x^{\frac{3}{4}}y^{\frac{3}{4}}}$

Answer:

$\frac{1}{8x^{\frac{3}{4}}y^{\frac{3}{4}}}$