# What is x in the equation 1000 = (x - 8) ^(3/2)?

Aug 6, 2018

$x = 108$

#### Explanation:

$1000 = {\left(x - 8\right)}^{\frac{3}{2}}$

Cube root both sides

$10 = {\left(x - 8\right)}^{\frac{1}{2}}$

Square both sides

$100 = x - 8$

$x = 108$

Aug 6, 2018

$x = 108$

#### Explanation:

${\left(x - 8\right)}^{\frac{3}{2}} = 1000$

${\left(x - 8\right)}^{\frac{3}{2}} = {10}^{3}$

${\left(x - 8\right)}^{3} = {10}^{6}$

$x - 8 = {10}^{2}$

$x = {10}^{2} + 8 = 108$

Aug 6, 2018

$x = 108$

#### Explanation:

Note that $1000 = {10}^{3}$

Raise both sides to the power of $\frac{2}{3}$

${\left({10}^{3}\right)}^{\frac{2}{3}} = {\left({\left(x - 8\right)}^{\frac{3}{2}}\right)}^{\frac{2}{3}}$

Multiply the indices:

${10}^{2} = x - 8$

$100 = x - 8$

$108 = x$

Aug 7, 2018

color(maroon)(x = 108

#### Explanation:

$1000 = {\left(x - 8\right)}^{\frac{3}{2}}$

${10}^{3} = {\left(x - 8\right)}^{\frac{3}{2}}$

${\left({100}^{\frac{1}{2}}\right)}^{3} = {\left(x - 8\right)}^{\frac{3}{2}}$

${100}^{\frac{3}{2}} = {\left(x - 8\right)}^{\frac{3}{2}}$

$100 = x - 8$

color(maroon)(x = 108