# How do you simplify 64^(log_4 (8y))?

Dec 31, 2015

$512 {y}^{3}$

#### Explanation:

$64 = {4}^{3}$, so the expression can be written as

$\implies {\left({4}^{3}\right)}^{{\log}_{4} \left(8 y\right)}$

$\implies {4}^{3 {\log}_{4} \left(8 y\right)}$

Rewrite using the rule: $a {\log}_{b} \left(c\right) = {\log}_{b} \left({c}^{a}\right)$

$\implies {4}^{{\log}_{4} \left({\left(8 y\right)}^{3}\right)}$

The $4$ and the ${\log}_{4}$ will cancel since exponentiation and logarithmic functions are inverses.

• ${a}^{{\log}_{a} \left(b\right)} = b$

$\implies {\left(8 y\right)}^{3}$

$\implies 512 {y}^{3}$