# How do you solve 3(x+3)^(3/4)= 81?

Apr 10, 2015

Simply divide by $3$:

${\left(x + 3\right)}^{\frac{3}{4}} = 27$

Raise everything to the $\frac{4}{3}$ to multiply by the $\frac{3}{4}$ to get $1$:

$x + 3 = {27}^{\frac{4}{3}}$

And subtract $3$.

$x = {27}^{\frac{4}{3}} - 3 = {3}^{3 \cdot \frac{4}{3}} - 3 = {3}^{4} - 3 = 78$

To check:
${\left(78 + 3\right)}^{\frac{3}{4}} = 27$
${81}^{\frac{3}{4}} = 27$
${3}^{3} = 27$