Question

simplify. $left(\frac{4a^{6}}{b^{-4}}\
ight)^{-3}$ write your answer using only positive exponents.

Explanation:

Step1: Rewrite negative denominator exponent

$\frac{4a^6}{b^{-4}} = 4a^6b^{4}$

Step2: Apply power to each term

$(4a^6b^{4})^{-3} = 4^{-3} \cdot (a^6)^{-3} \cdot (b^4)^{-3}$

Step3: Compute each exponent term

$4^{-3} = \frac{1}{4^3} = \frac{1}{64}$; $(a^6)^{-3} = a^{-18}$; $(b^4)^{-3} = b^{-12}$

Step4: Rewrite with positive exponents

$a^{-18} = \frac{1}{a^{18}}$; $b^{-12} = \frac{1}{b^{12}}$

Step5: Combine all terms

$\frac{1}{64} \cdot \frac{1}{a^{18}} \cdot \frac{1}{b^{12}} = \frac{1}{64a^{18}b^{12}}$

Answer:

$\frac{1}{64a^{18}b^{12}}$