Simplify (-6^(1/8)x^(1/4)y^(-1/4))^2

${(- 6^{\frac{1}{8}} x^{\frac{1}{4}} y^{\frac{- 1}{4}})}^{2}$

Step 1

Move the negative in front of the fraction.

${(- 6^{\frac{1}{8}} x^{\frac{1}{4}} y^{- \frac{1}{4}})}^{2}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(- 6^{\frac{1}{8}} x^{\frac{1}{4}} \frac{1}{y^{\frac{1}{4}}})}^{2}$

Step 3

Multiply $- 6^{\frac{1}{8}} x^{\frac{1}{4}} \frac{1}{y^{\frac{1}{4}}}$ .

Combine $6^{\frac{1}{8}}$ and $\frac{1}{y^{\frac{1}{4}}}$ .

${(- 1 x^{\frac{1}{4}} \frac{6^{\frac{1}{8}}}{y^{\frac{1}{4}}})}^{2}$

Combine $\frac{6^{\frac{1}{8}}}{y^{\frac{1}{4}}}$ and $x^{\frac{1}{4}}$ .

${(- 1 \frac{6^{\frac{1}{8}} x^{\frac{1}{4}}}{y^{\frac{1}{4}}})}^{2}$

Step 4

Rewrite $- 1 \frac{6^{\frac{1}{8}} x^{\frac{1}{4}}}{y^{\frac{1}{4}}}$ as $- \frac{6^{\frac{1}{8}} x^{\frac{1}{4}}}{y^{\frac{1}{4}}}$ .

${(- \frac{6^{\frac{1}{8}} x^{\frac{1}{4}}}{y^{\frac{1}{4}}})}^{2}$

Step 5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- \frac{6^{\frac{1}{8}} x^{\frac{1}{4}}}{y^{\frac{1}{4}}}$ .

${(- 1)}^{2} {(\frac{6^{\frac{1}{8}} x^{\frac{1}{4}}}{y^{\frac{1}{4}}})}^{2}$

Apply the product rule to $\frac{6^{\frac{1}{8}} x^{\frac{1}{4}}}{y^{\frac{1}{4}}}$ .

${(- 1)}^{2} \frac{{(6^{\frac{1}{8}} x^{\frac{1}{4}})}^{2}}{{(y^{\frac{1}{4}})}^{2}}$

Apply the product rule to $6^{\frac{1}{8}} x^{\frac{1}{4}}$ .

${(- 1)}^{2} \frac{{(6^{\frac{1}{8}})}^{2} {(x^{\frac{1}{4}})}^{2}}{{(y^{\frac{1}{4}})}^{2}}$

Step 6

Simplify the expression.

Raise $- 1$ to the power of $2$ .

$1 \frac{{(6^{\frac{1}{8}})}^{2} {(x^{\frac{1}{4}})}^{2}}{{(y^{\frac{1}{4}})}^{2}}$

Multiply $\frac{{(6^{\frac{1}{8}})}^{2} {(x^{\frac{1}{4}})}^{2}}{{(y^{\frac{1}{4}})}^{2}}$ by $1$ .

$\frac{{(6^{\frac{1}{8}})}^{2} {(x^{\frac{1}{4}})}^{2}}{{(y^{\frac{1}{4}})}^{2}}$

Step 7

Simplify the numerator.

Multiply the exponents in ${(6^{\frac{1}{8}})}^{2}$ .

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

$\frac{6^{\frac{1}{8} \cdot 2} {(x^{\frac{1}{4}})}^{2}}{{(y^{\frac{1}{4}})}^{2}}$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$\frac{6^{\frac{1}{2 (4)} \cdot 2} {(x^{\frac{1}{4}})}^{2}}{{(y^{\frac{1}{4}})}^{2}}$

Cancel the common factor.

$\frac{6^{\frac{1}{2 \cdot 4} \cdot 2} {(x^{\frac{1}{4}})}^{2}}{{(y^{\frac{1}{4}})}^{2}}$

Rewrite the expression.

$\frac{6^{\frac{1}{4}} {(x^{\frac{1}{4}})}^{2}}{{(y^{\frac{1}{4}})}^{2}}$

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

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

$\frac{6^{\frac{1}{4}} x^{\frac{1}{4} \cdot 2}}{{(y^{\frac{1}{4}})}^{2}}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{6^{\frac{1}{4}} x^{\frac{1}{2 (2)} \cdot 2}}{{(y^{\frac{1}{4}})}^{2}}$

Cancel the common factor.

$\frac{6^{\frac{1}{4}} x^{\frac{1}{2 \cdot 2} \cdot 2}}{{(y^{\frac{1}{4}})}^{2}}$

Rewrite the expression.

$\frac{6^{\frac{1}{4}} x^{\frac{1}{2}}}{{(y^{\frac{1}{4}})}^{2}}$

Step 8

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

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

$\frac{6^{\frac{1}{4}} x^{\frac{1}{2}}}{y^{\frac{1}{4} \cdot 2}}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{6^{\frac{1}{4}} x^{\frac{1}{2}}}{y^{\frac{1}{2 (2)} \cdot 2}}$

Cancel the common factor.

$\frac{6^{\frac{1}{4}} x^{\frac{1}{2}}}{y^{\frac{1}{2 \cdot 2} \cdot 2}}$

Rewrite the expression.

$\frac{6^{\frac{1}{4}} x^{\frac{1}{2}}}{y^{\frac{1}{2}}}$

Simplify (-6^(1/8)x^(1/4)y^(-1/4))^2

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