Algebra Examples

${(\frac{x^{\frac{1}{4}}}{y^{- \frac{3}{4}}})}^{12}$

Step 1

Move $y^{- \frac{3}{4}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(x^{\frac{1}{4}} y^{\frac{3}{4}})}^{12}$

Step 2

Apply the product rule to $x^{\frac{1}{4}} y^{\frac{3}{4}}$ .

${(x^{\frac{1}{4}})}^{12} {(y^{\frac{3}{4}})}^{12}$

Step 3

Multiply the exponents in ${(x^{\frac{1}{4}})}^{12}$ .

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Step 3.1

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

$x^{\frac{1}{4} \cdot 12} {(y^{\frac{3}{4}})}^{12}$

Step 3.2

Cancel the common factor of $4$ .

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Step 3.2.1

Factor $4$ out of $12$ .

$x^{\frac{1}{4} \cdot (4 (3))} {(y^{\frac{3}{4}})}^{12}$

Step 3.2.2

Cancel the common factor.

$x^{\frac{1}{4} \cdot (4 \cdot 3)} {(y^{\frac{3}{4}})}^{12}$

Step 3.2.3

Rewrite the expression.

$x^{3} {(y^{\frac{3}{4}})}^{12}$

Step 4

Multiply the exponents in ${(y^{\frac{3}{4}})}^{12}$ .

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Step 4.1

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

$x^{3} y^{\frac{3}{4} \cdot 12}$

Step 4.2

Cancel the common factor of $4$ .

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Step 4.2.1

Factor $4$ out of $12$ .

$x^{3} y^{\frac{3}{4} \cdot (4 (3))}$

Step 4.2.2

Cancel the common factor.

$x^{3} y^{\frac{3}{4} \cdot (4 \cdot 3)}$

Step 4.2.3

Rewrite the expression.

$x^{3} y^{3 \cdot 3}$

Step 4.3

Multiply $3$ by $3$ .

$x^{3} y^{9}$