Solve for x -1080=-5x^(3/2)

$- 1080 = - 5 x^{\frac{3}{2}}$

Step 1

Rewrite the equation as $- 5 x^{\frac{3}{2}} = - 1080$ .

$- 5 x^{\frac{3}{2}} = - 1080$

Step 2

Divide each term in $- 5 x^{\frac{3}{2}} = - 1080$ by $- 5$ and simplify.

Divide each term in $- 5 x^{\frac{3}{2}} = - 1080$ by $- 5$ .

$\frac{- 5 x^{\frac{3}{2}}}{- 5} = \frac{- 1080}{- 5}$

Simplify the left side.

Cancel the common factor.

$\frac{- 5 x^{\frac{3}{2}}}{- 5} = \frac{- 1080}{- 5}$

Divide $x^{\frac{3}{2}}$ by $1$ .

$x^{\frac{3}{2}} = \frac{- 1080}{- 5}$

Simplify the right side.

Divide $- 1080$ by $- 5$ .

$x^{\frac{3}{2}} = 216$

Step 3

Raise each side of the equation to the power of $\frac{2}{3}$ to eliminate the fractional exponent on the left side.

${(x^{\frac{3}{2}})}^{\frac{2}{3}} = 216^{\frac{2}{3}}$

Step 4

Simplify the exponent.

Simplify the left side.

Simplify ${(x^{\frac{3}{2}})}^{\frac{2}{3}}$ .

Multiply the exponents in ${(x^{\frac{3}{2}})}^{\frac{2}{3}}$ .

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

$x^{\frac{3}{2} \cdot \frac{2}{3}} = 216^{\frac{2}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$x^{\frac{3}{2} \cdot \frac{2}{3}} = 216^{\frac{2}{3}}$

Rewrite the expression.

$x^{\frac{1}{2} \cdot 2} = 216^{\frac{2}{3}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 216^{\frac{2}{3}}$

Rewrite the expression.

$x^{1} = 216^{\frac{2}{3}}$

Simplify.

$x = 216^{\frac{2}{3}}$

Simplify the right side.

Simplify $216^{\frac{2}{3}}$ .

Simplify the expression.

Rewrite $216$ as $6^{3}$ .

$x = {(6^{3})}^{\frac{2}{3}}$

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

$x = 6^{3 (\frac{2}{3})}$

Cancel the common factor of $3$ .

Cancel the common factor.

$x = 6^{3 (\frac{2}{3})}$

Rewrite the expression.

$x = 6^{2}$

Raise $6$ to the power of $2$ .

$x = 36$

Solve for x -1080=-5x^(3/2)

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