Simplify ((a^(3/8))/(a^(1/8)))^2

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Algebra

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Subtract $1$ from $3$ .

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

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

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Factor $2$ out of $2$ .

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

Cancel the common factors.

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Factor $2$ out of $8$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Cancel the common factor of $2$ .

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Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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