Algebra Examples

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

Step 1

Multiply $y^{\frac{4}{3}}$ by $y^{\frac{2}{3}}$ by adding the exponents.

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Step 1.1

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

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

Step 1.2

Combine the numerators over the common denominator.

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

Step 1.3

Add $4$ and $2$ .

${(y^{\frac{6}{3}})}^{- \frac{1}{2}}$

Step 1.4

Divide $6$ by $3$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

$y^{- 1}$

Step 3

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

$\frac{1}{y}$