Algebra Examples

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

Step 1

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

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

Step 2

Multiply $a^{\frac{3}{8}}$ by $a^{- \frac{1}{8}}$ 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.

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 2.3

Subtract $1$ from $3$ .

${(a^{\frac{2}{8}})}^{2}$

Step 2.4

Cancel the common factor of $2$ and $8$ .

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Step 2.4.1

Factor $2$ out of $2$ .

${(a^{\frac{2 (1)}{8}})}^{2}$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $2$ out of $8$ .

${(a^{\frac{2 \cdot 1}{2 \cdot 4}})}^{2}$

Step 2.4.2.2

Cancel the common factor.

${(a^{\frac{2 \cdot 1}{2 \cdot 4}})}^{2}$

Step 2.4.2.3

Rewrite the expression.

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

Step 3

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

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Step 3.1

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

$a^{\frac{1}{4} \cdot 2}$

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Factor $2$ out of $4$ .

$a^{\frac{1}{2 (2)} \cdot 2}$

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

$a^{\frac{1}{2}}$