Simplify ((x^2yz^0)/(3x^6y^-4))^4

${(\frac{x^{2} y z^{0}}{3 x^{6} y^{- 4}})}^{4}$

Step 1

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

${(\frac{x^{2} y z^{0} y^{4}}{3 x^{6}})}^{4}$

Step 2

Simplify the numerator.

Multiply $y$ by $y^{4}$ by adding the exponents.

Move $y^{4}$ .

${(\frac{x^{2} (y^{4} y) z^{0}}{3 x^{6}})}^{4}$

Multiply $y^{4}$ by $y$ .

Raise $y$ to the power of $1$ .

${(\frac{x^{2} (y^{4} y^{1}) z^{0}}{3 x^{6}})}^{4}$

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

${(\frac{x^{2} y^{4 + 1} z^{0}}{3 x^{6}})}^{4}$

Add $4$ and $1$ .

${(\frac{x^{2} y^{5} z^{0}}{3 x^{6}})}^{4}$

Simplify $x^{2} y^{5} z^{0}$ .

${(\frac{x^{2} y^{5}}{3 x^{6}})}^{4}$

Step 3

Cancel the common factor of $x^{2}$ and $x^{6}$ .

Factor $x^{2}$ out of $x^{2} y^{5}$ .

${(\frac{x^{2} (y^{5})}{3 x^{6}})}^{4}$

Cancel the common factors.

Factor $x^{2}$ out of $3 x^{6}$ .

${(\frac{x^{2} (y^{5})}{x^{2} (3 x^{4})})}^{4}$

Cancel the common factor.

${(\frac{x^{2} y^{5}}{x^{2} (3 x^{4})})}^{4}$

Rewrite the expression.

${(\frac{y^{5}}{3 x^{4}})}^{4}$

Step 4

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

Apply the product rule to $\frac{y^{5}}{3 x^{4}}$ .

$\frac{{(y^{5})}^{4}}{{(3 x^{4})}^{4}}$

Apply the product rule to $3 x^{4}$ .

$\frac{{(y^{5})}^{4}}{3^{4} {(x^{4})}^{4}}$

Step 5

Multiply the exponents in ${(y^{5})}^{4}$ .

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

$\frac{y^{5 \cdot 4}}{3^{4} {(x^{4})}^{4}}$

Multiply $5$ by $4$ .

$\frac{y^{20}}{3^{4} {(x^{4})}^{4}}$

Step 6

Simplify the denominator.

Raise $3$ to the power of $4$ .

$\frac{y^{20}}{81 {(x^{4})}^{4}}$

Multiply the exponents in ${(x^{4})}^{4}$ .

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

$\frac{y^{20}}{81 x^{4 \cdot 4}}$

Multiply $4$ by $4$ .

$\frac{y^{20}}{81 x^{16}}$

Simplify ((x^2yz^0)/(3x^6y^-4))^4

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