Solve by Factoring 2x^(5/3)=-64

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

Step 1

Add $64$ to both sides of the equation.

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

Step 2

Factor $2$ out of $2 x^{\frac{5}{3}} + 64$ .

Factor $2$ out of $2 x^{\frac{5}{3}}$ .

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

Factor $2$ out of $64$ .

$2 x^{\frac{5}{3}} + 2 \cdot 32 = 0$

Factor $2$ out of $2 x^{\frac{5}{3}} + 2 \cdot 32$ .

$2 (x^{\frac{5}{3}} + 32) = 0$

Step 3

Divide each term in $2 (x^{\frac{5}{3}} + 32) = 0$ by $2$ and simplify.

Divide each term in $2 (x^{\frac{5}{3}} + 32) = 0$ by $2$ .

$\frac{2 (x^{\frac{5}{3}} + 32)}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor.

$\frac{2 (x^{\frac{5}{3}} + 32)}{2} = \frac{0}{2}$

Divide $x^{\frac{5}{3}} + 32$ by $1$ .

$x^{\frac{5}{3}} + 32 = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$x^{\frac{5}{3}} + 32 = 0$

Step 4

Subtract $32$ from both sides of the equation.

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

Step 5

Raise each side of the equation to the power of $\frac{3}{5}$ to eliminate the fractional exponent on the left side.

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

Step 6

Simplify the exponent.

Simplify the left side.

Simplify ${(x^{\frac{5}{3}})}^{\frac{3}{5}}$ .

Multiply the exponents in ${(x^{\frac{5}{3}})}^{\frac{3}{5}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

Simplify ${(- 32)}^{\frac{3}{5}}$ .

Simplify the expression.

Rewrite $- 32$ as ${(- 2)}^{5}$ .

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

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

$x = {(- 2)}^{3}$

Raise $- 2$ to the power of $3$ .

$x = - 8$

Solve by Factoring 2x^(5/3)=-64

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