Solve for a a^(3/2)=-27

$a^{\frac{3}{2}} = - 27$

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

${(a^{\frac{3}{2}})}^{\frac{2}{3}} = {(- 27)}^{\frac{2}{3}}$

Simplify ${(- 27)}^{\frac{2}{3}}$ .

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Simplify the expression.

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Rewrite $- 27$ as ${(- 3)}^{3}$ .

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

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

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

Cancel the common factor of $3$ .

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Cancel the common factor.

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

Rewrite the expression.

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

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

$a = 9$

Exclude the solutions that do not make $a^{\frac{3}{2}} = - 27$ true.

No solution

Solve for a a^(3/2)=-27

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