Solve for n (x^3)^3=x^n

${(x^{3})}^{3} = x^{n}$

Step 1

Rewrite the equation as $x^{n} = {(x^{3})}^{3}$ .

$x^{n} = {(x^{3})}^{3}$

Step 2

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

$x^{n} = x^{3 \cdot 3}$

Step 3

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

$n = 3 \cdot 3$

Step 4

Multiply $3$ by $3$ .

$n = 9$