Pre-Algebra Examples

${(\frac{x^{6} y^{- 6}}{x^{8} y^{- 8}})}^{\frac{1}{2}}$

Step 1

Move $y^{- 8}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{x^{6} y^{- 6} y^{8}}{x^{8}})}^{\frac{1}{2}}$

Step 2

Multiply $y^{- 6}$ by $y^{8}$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $y^{8}$ .

${(\frac{x^{6} (y^{8} y^{- 6})}{x^{8}})}^{\frac{1}{2}}$

Step 2.2

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

${(\frac{x^{6} y^{8 - 6}}{x^{8}})}^{\frac{1}{2}}$

Step 2.3

Subtract $6$ from $8$ .

${(\frac{x^{6} y^{2}}{x^{8}})}^{\frac{1}{2}}$

Step 3

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 3.1

Cancel the common factor of $x^{6}$ and $x^{8}$ .

Tap for more steps...

Step 3.1.1

Factor $x^{6}$ out of $x^{6} y^{2}$ .

${(\frac{x^{6} (y^{2})}{x^{8}})}^{\frac{1}{2}}$

Step 3.1.2

Cancel the common factors.

Tap for more steps...

Step 3.1.2.1

Factor $x^{6}$ out of $x^{8}$ .

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

Step 3.1.2.2

Cancel the common factor.

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

Step 3.1.2.3

Rewrite the expression.

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

Step 3.2

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

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

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

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

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

Step 4.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.1.2.1

Cancel the common factor.

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

Step 4.1.2.2

Rewrite the expression.

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

Step 4.2

Simplify.

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

Step 5

Simplify the denominator.

Tap for more steps...

Step 5.1

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

Tap for more steps...

Step 5.1.1

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

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

Step 5.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 5.1.2.1

Cancel the common factor.

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

Step 5.1.2.2

Rewrite the expression.

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

Step 5.2

Simplify.

$\frac{y}{x}$