Solve for a 29.5=a^(3/2)

$29.5 = a^{\frac{3}{2}}$

Step 1

Rewrite the equation as $a^{\frac{3}{2}} = 29.5$ .

$a^{\frac{3}{2}} = 29.5$

Step 2

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

${(a^{\frac{3}{2}})}^{\frac{2}{3}} = {29.5}^{\frac{2}{3}}$

Step 3

Simplify the exponent.

Simplify the left side.

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

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

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

$a^{\frac{3}{2} \cdot \frac{2}{3}} = {29.5}^{\frac{2}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$a^{\frac{3}{2} \cdot \frac{2}{3}} = {29.5}^{\frac{2}{3}}$

Rewrite the expression.

$a^{\frac{1}{2} \cdot 2} = {29.5}^{\frac{2}{3}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$a^{\frac{1}{2} \cdot 2} = {29.5}^{\frac{2}{3}}$

Rewrite the expression.

$a^{1} = {29.5}^{\frac{2}{3}}$

Simplify.

$a = {29.5}^{\frac{2}{3}}$

Simplify the right side.

Raise $29.5$ to the power of $\frac{2}{3}$ .

$a = 9.54731702$