# The given equation involves a power of the variable. Find all real solutions of the...

tricotasu

## Answered question

2021-09-11

The given equation involves a power of the variable. Find all real solutions of the equation.

$2{x}^{\frac{5}{3}}+64=0$

### Answer & Explanation

Step 1

The given equation is $2{x}^{\frac{5}{3}}+64=0$

Step 2

$2{x}^{\frac{5}{3}}+64=0$

$2{x}^{\frac{5}{3}}=-64$

${x}^{\frac{5}{3}}=-32$

$\left({x}^{\frac{5}{3}}\right)}^{\frac{1}{5}}={(-32)}^{\frac{1}{5}$

${x}^{\frac{1}{3}}=-2$

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

x=-8

Answer is given below (on video)

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