Simplify (a^8)^(3/2)

${(a^{8})}^{\frac{3}{2}}$

Step 1

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

$a^{8 (\frac{3}{2})}$

Step 2

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$a^{2 (4) \frac{3}{2}}$

Cancel the common factor.

$a^{2 \cdot 4 \frac{3}{2}}$

Rewrite the expression.

$a^{4 \cdot 3}$

Step 3

Multiply $4$ by $3$ .

$a^{12}$