Algebra Examples

{(\frac{1}{q^{- 8} \cdot q^{2}})}^{\frac{1}{8}}

${(\frac{1}{q^{- 8} \cdot q^{2}})}^{\frac{1}{8}}$

Step 1

Multiply

q^{- 8}

$q^{- 8}$ by

q^{2}

$q^{2}$ by adding the exponents.

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Step 1.1

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

{(\frac{1}{q^{- 8 + 2}})}^{\frac{1}{8}}

${(\frac{1}{q^{- 8 + 2}})}^{\frac{1}{8}}$

Step 1.2

Add

- 8

$- 8$ and

2

$2$ .

{(\frac{1}{q^{- 6}})}^{\frac{1}{8}}

${(\frac{1}{q^{- 6}})}^{\frac{1}{8}}$

{(\frac{1}{q^{- 6}})}^{\frac{1}{8}}

${(\frac{1}{q^{- 6}})}^{\frac{1}{8}}$

Step 2

Move

q^{- 6}

$q^{- 6}$ to the numerator using the negative exponent rule

\frac{1}{b^{- n}} = b^{n}

$\frac{1}{b^{- n}} = b^{n}$ .

{(q^{6})}^{\frac{1}{8}}

${(q^{6})}^{\frac{1}{8}}$

Step 3

Multiply the exponents in

{(q^{6})}^{\frac{1}{8}}

${(q^{6})}^{\frac{1}{8}}$ .

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Step 3.1

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

q^{6 (\frac{1}{8})}

$q^{6 (\frac{1}{8})}$

Step 3.2

Cancel the common factor of

2

$2$ .

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Step 3.2.1

Factor

2

$2$ out of

6

$6$ .

q^{2 (3) \frac{1}{8}}

$q^{2 (3) \frac{1}{8}}$

Step 3.2.2

Factor

2

$2$ out of

8

$8$ .

q^{2 \cdot 3 \frac{1}{2 \cdot 4}}

$q^{2 \cdot 3 \frac{1}{2 \cdot 4}}$

Step 3.2.3

Cancel the common factor.

$q^{2 \cdot 3 \frac{1}{2 \cdot 4}}$

Step 3.2.4

Rewrite the expression.

$q^{3 (\frac{1}{4})}$

$q^{3 (\frac{1}{4})}$

Step 3.3

Combine

$3$ and

$\frac{1}{4}$ .

$q^{\frac{3}{4}}$

$q^{\frac{3}{4}}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$