Solve for x -96=3(8x)^(5/3)

$- 96 = 3 {(8 x)}^{\frac{5}{3}}$

Rewrite the equation as $3 {(8 x)}^{\frac{5}{3}} = - 96$ .

$3 {(8 x)}^{\frac{5}{3}} = - 96$

Divide each term in $3 {(8 x)}^{\frac{5}{3}} = - 96$ by $3$ and simplify.

Divide each term in $3 {(8 x)}^{\frac{5}{3}} = - 96$ by $3$ .

$\frac{3 {(8 x)}^{\frac{5}{3}}}{3} = \frac{- 96}{3}$

Simplify the left side.

Cancel the common factor.

$\frac{3 {(8 x)}^{\frac{5}{3}}}{3} = \frac{- 96}{3}$

Simplify the expression.

Divide ${(8 x)}^{\frac{5}{3}}$ by $1$ .

${(8 x)}^{\frac{5}{3}} = \frac{- 96}{3}$

Apply the product rule to $8 x$ .

$8^{\frac{5}{3}} x^{\frac{5}{3}} = \frac{- 96}{3}$

Rewrite $8$ as $2^{3}$ .

${(2^{3})}^{\frac{5}{3}} x^{\frac{5}{3}} = \frac{- 96}{3}$

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

$2^{3 (\frac{5}{3})} x^{\frac{5}{3}} = \frac{- 96}{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$2^{3 (\frac{5}{3})} x^{\frac{5}{3}} = \frac{- 96}{3}$

Rewrite the expression.

$2^{5} x^{\frac{5}{3}} = \frac{- 96}{3}$

Raise $2$ to the power of $5$ .

$32 x^{\frac{5}{3}} = \frac{- 96}{3}$

Simplify the right side.

Divide $- 96$ by $3$ .

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

Divide each term in $32 x^{\frac{5}{3}} = - 32$ by $32$ and simplify.

Divide each term in $32 x^{\frac{5}{3}} = - 32$ by $32$ .

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

Simplify the left side.

Cancel the common factor.

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

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

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

Simplify the right side.

Divide $- 32$ by $32$ .

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

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

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

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, ${(a^{m})}^{n} = a^{m n}$ .

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

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

Simplify ${(- 1)}^{\frac{3}{5}}$ .

Simplify the expression.

Rewrite $- 1$ as ${(- 1)}^{5}$ .

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

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

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

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

$x = {(- 1)}^{3}$

Raise $- 1$ to the power of $3$ .

$x = - 1$

Solve for x -96=3(8x)^(5/3)

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