# How do you solve (2x+7)^(3/2)=27?

Mar 19, 2016

We must first convert to radical form by using the exponent rule ${a}^{\frac{m}{n}} = \sqrt[n]{{a}^{m}}$

#### Explanation:

$\sqrt{{\left(2 x + 7\right)}^{3}} = 27$

We can get rid of the radical by squaring both sides of the equation.

${\left(2 x + 7\right)}^{3} = 729$

Now, to cancel the cube, we must take the cube root of $729$.

$2 x + 7 = 9$

$2 x = 2$

$x = \frac{2}{2}$

$x = 1$

Practice exercises:

Solve for x:

a). ${\left(2 x + 1\right)}^{\frac{3}{2}} = 7 x - 1$

b). ${8}^{\frac{x}{3}} = 3 x + 4$

Good luck!