Algebra Examples

$\frac{{(16 x^{2} y^{- 1})}^{0}}{{(4 x^{0} y^{- 4} z)}^{- 2}}$

Step 1

Move ${(4 x^{0} y^{- 4} z)}^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(16 x^{2} y^{- 1})}^{0} {(4 x^{0} y^{- 4} z)}^{2}$

Step 2

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

${(16 x^{2} \frac{1}{y})}^{0} {(4 x^{0} y^{- 4} z)}^{2}$

Step 3

Multiply $16 x^{2} \frac{1}{y}$ .

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Step 3.1

Combine $16$ and $\frac{1}{y}$ .

${(x^{2} \frac{16}{y})}^{0} {(4 x^{0} y^{- 4} z)}^{2}$

Step 3.2

Combine $x^{2}$ and $\frac{16}{y}$ .

${(\frac{x^{2} \cdot 16}{y})}^{0} {(4 x^{0} y^{- 4} z)}^{2}$

Step 4

Move $16$ to the left of $x^{2}$ .

${(\frac{16 \cdot x^{2}}{y})}^{0} {(4 x^{0} y^{- 4} z)}^{2}$

Step 5

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

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Step 5.1

Apply the product rule to $\frac{16 x^{2}}{y}$ .

$\frac{{(16 x^{2})}^{0}}{y^{0}} {(4 x^{0} y^{- 4} z)}^{2}$

Step 5.2

Apply the product rule to $16 x^{2}$ .

$\frac{16^{0} {(x^{2})}^{0}}{y^{0}} {(4 x^{0} y^{- 4} z)}^{2}$

Step 6

Simplify the numerator.

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Step 6.1

Anything raised to $0$ is $1$ .

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

Step 6.2

Multiply the exponents in ${(x^{2})}^{0}$ .

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Step 6.2.1

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

$\frac{1 x^{2 \cdot 0}}{y^{0}} {(4 x^{0} y^{- 4} z)}^{2}$

Step 6.2.2

Multiply $2$ by $0$ .

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

Step 6.3

Anything raised to $0$ is $1$ .

$\frac{1 \cdot 1}{y^{0}} {(4 x^{0} y^{- 4} z)}^{2}$

Step 6.4

Multiply $1$ by $1$ .

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

Step 7

Simplify the expression.

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Step 7.1

Anything raised to $0$ is $1$ .

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

Step 7.2

Divide $1$ by $1$ .

$1 {(4 x^{0} y^{- 4} z)}^{2}$

Step 7.3

Multiply ${(4 x^{0} y^{- 4} z)}^{2}$ by $1$ .

${(4 x^{0} y^{- 4} z)}^{2}$

Step 7.4

Anything raised to $0$ is $1$ .

${(4 \cdot 1 y^{- 4} z)}^{2}$

Step 7.5

Multiply $4$ by $1$ .

${(4 y^{- 4} z)}^{2}$

Step 8

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

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

Step 9

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

${(\frac{4}{y^{4}} z)}^{2}$

Step 10

Combine $\frac{4}{y^{4}}$ and $z$ .

${(\frac{4 z}{y^{4}})}^{2}$

Step 11

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

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Step 11.1

Apply the product rule to $\frac{4 z}{y^{4}}$ .

$\frac{{(4 z)}^{2}}{{(y^{4})}^{2}}$

Step 11.2

Apply the product rule to $4 z$ .

$\frac{4^{2} z^{2}}{{(y^{4})}^{2}}$

Step 12

Raise $4$ to the power of $2$ .

$\frac{16 z^{2}}{{(y^{4})}^{2}}$

Step 13

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

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Step 13.1

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

$\frac{16 z^{2}}{y^{4 \cdot 2}}$

Step 13.2

Multiply $4$ by $2$ .

$\frac{16 z^{2}}{y^{8}}$