Simplify ((j^2j^5)/(j^4))^3

${(\frac{j^{2} j^{5}}{j^{4}})}^{3}$

Step 1

Multiply $j^{2}$ by $j^{5}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{j^{2 + 5}}{j^{4}})}^{3}$

Add $2$ and $5$ .

${(\frac{j^{7}}{j^{4}})}^{3}$

Step 2

Cancel the common factor of $j^{7}$ and $j^{4}$ .

Factor $j^{4}$ out of $j^{7}$ .

${(\frac{j^{4} j^{3}}{j^{4}})}^{3}$

Cancel the common factors.

Multiply by $1$ .

${(\frac{j^{4} j^{3}}{j^{4} \cdot 1})}^{3}$

Cancel the common factor.

${(\frac{j^{4} j^{3}}{j^{4} \cdot 1})}^{3}$

Rewrite the expression.

${(\frac{j^{3}}{1})}^{3}$

Divide $j^{3}$ by $1$ .

${(j^{3})}^{3}$

Step 3

Multiply the exponents in ${(j^{3})}^{3}$ .

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

$j^{3 \cdot 3}$

Multiply $3$ by $3$ .

$j^{9}$