Simplify (9x^4y^-2)^(1/2)

${(9 x^{4} y^{- 2})}^{\frac{1}{2}}$

Step 1

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

${(9 x^{4} \frac{1}{y^{2}})}^{\frac{1}{2}}$

Step 2

Multiply $9 x^{4} \frac{1}{y^{2}}$ .

Combine $9$ and $\frac{1}{y^{2}}$ .

${(x^{4} \frac{9}{y^{2}})}^{\frac{1}{2}}$

Combine $x^{4}$ and $\frac{9}{y^{2}}$ .

${(\frac{x^{4} \cdot 9}{y^{2}})}^{\frac{1}{2}}$

Step 3

Move $9$ to the left of $x^{4}$ .

${(\frac{9 \cdot x^{4}}{y^{2}})}^{\frac{1}{2}}$

Step 4

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

Apply the product rule to $\frac{9 x^{4}}{y^{2}}$ .

$\frac{{(9 x^{4})}^{\frac{1}{2}}}{{(y^{2})}^{\frac{1}{2}}}$

Apply the product rule to $9 x^{4}$ .

$\frac{9^{\frac{1}{2}} {(x^{4})}^{\frac{1}{2}}}{{(y^{2})}^{\frac{1}{2}}}$

Step 5

Simplify the numerator.

Rewrite $9$ as $3^{2}$ .

$\frac{{(3^{2})}^{\frac{1}{2}} {(x^{4})}^{\frac{1}{2}}}{{(y^{2})}^{\frac{1}{2}}}$

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

$\frac{3^{2 (\frac{1}{2})} {(x^{4})}^{\frac{1}{2}}}{{(y^{2})}^{\frac{1}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3^{2 (\frac{1}{2})} {(x^{4})}^{\frac{1}{2}}}{{(y^{2})}^{\frac{1}{2}}}$

Rewrite the expression.

$\frac{3^{1} {(x^{4})}^{\frac{1}{2}}}{{(y^{2})}^{\frac{1}{2}}}$

Evaluate the exponent.

$\frac{3 {(x^{4})}^{\frac{1}{2}}}{{(y^{2})}^{\frac{1}{2}}}$

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

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

$\frac{3 x^{4 (\frac{1}{2})}}{{(y^{2})}^{\frac{1}{2}}}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{3 x^{2 (2) \frac{1}{2}}}{{(y^{2})}^{\frac{1}{2}}}$

Cancel the common factor.

$\frac{3 x^{2 \cdot 2 \frac{1}{2}}}{{(y^{2})}^{\frac{1}{2}}}$

Rewrite the expression.

$\frac{3 x^{2}}{{(y^{2})}^{\frac{1}{2}}}$

Step 6

Simplify the denominator.

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

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

$\frac{3 x^{2}}{y^{2 (\frac{1}{2})}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3 x^{2}}{y^{2 (\frac{1}{2})}}$

Rewrite the expression.

$\frac{3 x^{2}}{y^{1}}$

Simplify.

$\frac{3 x^{2}}{y}$

Simplify (9x^4y^-2)^(1/2)

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