Solve for x (2^x)^5=2^15

${(2^{x})}^{5} = 2^{15}$

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

$2^{x \cdot 5} = 2^{15}$

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

$x \cdot 5 = 15$

Divide each term in $(x \cdot 5) = 15$ by $5$ and simplify.

Divide each term in $(x \cdot 5) = 15$ by $5$ .

$\frac{(x \cdot 5)}{5} = \frac{15}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{x \cdot 5}{5} = \frac{15}{5}$

Divide $x$ by $1$ .

$x = \frac{15}{5}$

Simplify the right side.

Divide $15$ by $5$ .

$x = 3$