Solve for a (b^2)^a=b^8

${(b^{2})}^{a} = b^{8}$

Step 1

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

$b^{2 a} = b^{8}$

Step 2

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$2 a = 8$

Step 3

Divide each term in $2 a = 8$ by $2$ and simplify.

Divide each term in $2 a = 8$ by $2$ .

$\frac{2 a}{2} = \frac{8}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 a}{2} = \frac{8}{2}$

Divide $a$ by $1$ .

$a = \frac{8}{2}$

Simplify the right side.

Divide $8$ by $2$ .

$a = 4$