Algebra Examples

${(x^{3} y^{- 2})}^{4}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(x^{3} \frac{1}{y^{2}})}^{4}$

Step 2

Combine $x^{3}$ and $\frac{1}{y^{2}}$ .

${(\frac{x^{3}}{y^{2}})}^{4}$

Step 3

Apply basic rules of exponents.

Tap for more steps...

Step 3.1

Apply the product rule to $\frac{x^{3}}{y^{2}}$ .

$\frac{{(x^{3})}^{4}}{{(y^{2})}^{4}}$

Step 3.2

Multiply the exponents in ${(x^{3})}^{4}$ .

Tap for more steps...

Step 3.2.1

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

$\frac{x^{3 \cdot 4}}{{(y^{2})}^{4}}$

Step 3.2.2

Multiply $3$ by $4$ .

$\frac{x^{12}}{{(y^{2})}^{4}}$

Step 3.3

Multiply the exponents in ${(y^{2})}^{4}$ .

Tap for more steps...

Step 3.3.1

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

$\frac{x^{12}}{y^{2 \cdot 4}}$

Step 3.3.2

Multiply $2$ by $4$ .

$\frac{x^{12}}{y^{8}}$