Algebra Examples

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

Step 1

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Step 2

Apply basic rules of exponents.

Tap for more steps...

Step 2.1

Apply the product rule to $\frac{y^{\frac{1}{3}}}{x^{2}}$ .

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

Step 2.2

Multiply the exponents in ${(y^{\frac{1}{3}})}^{\frac{1}{2}}$ .

Tap for more steps...

Step 2.2.1

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

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

Step 2.2.2

Multiply $\frac{1}{3} \cdot \frac{1}{2}$ .

Tap for more steps...

Step 2.2.2.1

Multiply $\frac{1}{3}$ by $\frac{1}{2}$ .

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

Step 2.2.2.2

Multiply $3$ by $2$ .

$\frac{y^{\frac{1}{6}}}{{(x^{2})}^{\frac{1}{2}}}$

Step 3

Simplify the denominator.

Tap for more steps...

Step 3.1

Multiply the exponents in ${(x^{2})}^{\frac{1}{2}}$ .

Tap for more steps...

Step 3.1.1

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

$\frac{y^{\frac{1}{6}}}{x^{2 (\frac{1}{2})}}$

Step 3.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.1.2.1

Cancel the common factor.

$\frac{y^{\frac{1}{6}}}{x^{2 (\frac{1}{2})}}$

Step 3.1.2.2

Rewrite the expression.

$\frac{y^{\frac{1}{6}}}{x^{1}}$

Step 3.2

Simplify.

$\frac{y^{\frac{1}{6}}}{x}$