Trigonometry Examples

${(\frac{w^{- 5}}{w^{- 9}})}^{\frac{1}{2}}$

Step 1

Move $w^{- 9}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(w^{- 5} w^{9})}^{\frac{1}{2}}$

Step 2

Multiply $w^{- 5}$ by $w^{9}$ by adding the exponents.

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Step 2.1

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

${(w^{- 5 + 9})}^{\frac{1}{2}}$

Step 2.2

Add $- 5$ and $9$ .

${(w^{4})}^{\frac{1}{2}}$

Step 3

Multiply the exponents in ${(w^{4})}^{\frac{1}{2}}$ .

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Step 3.1

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

$w^{4 (\frac{1}{2})}$

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Factor $2$ out of $4$ .

$w^{2 (2) \frac{1}{2}}$

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

$w^{2}$