Algebra Examples

${(w^{- 7} \cdot w^{- 6})}^{\frac{3}{26}}$

Step 1

Multiply $w^{- 7}$ by $w^{- 6}$ 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.

${(w^{- 7 - 6})}^{\frac{3}{26}}$

Step 1.2

Subtract $6$ from $- 7$ .

${(w^{- 13})}^{\frac{3}{26}}$

Step 2

Multiply the exponents in ${(w^{- 13})}^{\frac{3}{26}}$ .

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Step 2.1

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

$w^{- 13 (\frac{3}{26})}$

Step 2.2

Cancel the common factor of $13$ .

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Step 2.2.1

Factor $13$ out of $- 13$ .

$w^{13 (- 1) \frac{3}{26}}$

Step 2.2.2

Factor $13$ out of $26$ .

$w^{13 \cdot - 1 \frac{3}{13 \cdot 2}}$

Step 2.2.3

Cancel the common factor.

$w^{13 \cdot - 1 \frac{3}{13 \cdot 2}}$

Step 2.2.4

Rewrite the expression.

$w^{- \frac{3}{2}}$

Step 3

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

$\frac{1}{w^{\frac{3}{2}}}$