Simplify ((9y^2)/(x^-8y^0))^(1/2)

${(\frac{9 y^{2}}{x^{- 8} y^{0}})}^{\frac{1}{2}}$

Step 1

Move $y^{0}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{9 y^{2} y^{0}}{x^{- 8}})}^{\frac{1}{2}}$

Step 2

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

${(9 y^{2} y^{0} x^{8})}^{\frac{1}{2}}$

Step 3

Multiply $y^{2}$ by $y^{0}$ by adding the exponents.

Move $y^{0}$ .

${(9 (y^{0} y^{2}) x^{8})}^{\frac{1}{2}}$

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

${(9 y^{0 + 2} x^{8})}^{\frac{1}{2}}$

Add $0$ and $2$ .

${(9 y^{2} x^{8})}^{\frac{1}{2}}$

Step 4

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

Apply the product rule to $9 y^{2} x^{8}$ .

${(9 y^{2})}^{\frac{1}{2}} {(x^{8})}^{\frac{1}{2}}$

Apply the product rule to $9 y^{2}$ .

$9^{\frac{1}{2}} {(y^{2})}^{\frac{1}{2}} {(x^{8})}^{\frac{1}{2}}$

Step 5

Simplify the expression.

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

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

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

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

Step 6

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 7

Evaluate the exponent.

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

Step 8

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 9

Simplify.

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

Step 10

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

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

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

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

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

Cancel the common factor.

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

Rewrite the expression.

$3 y x^{4}$

Simplify ((9y^2)/(x^-8y^0))^(1/2)

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