Algebra Examples

${(- 18 x^{5} y^{- 2})}^{0}$

Step 1

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

${(- 18 x^{5} \frac{1}{y^{2}})}^{0}$

Step 2

Multiply $- 18 x^{5} \frac{1}{y^{2}}$ .

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Step 2.1

Combine $- 18$ and $\frac{1}{y^{2}}$ .

${(x^{5} \frac{- 18}{y^{2}})}^{0}$

Step 2.2

Combine $x^{5}$ and $\frac{- 18}{y^{2}}$ .

${(\frac{x^{5} \cdot - 18}{y^{2}})}^{0}$

Step 3

Move $- 18$ to the left of $x^{5}$ .

${(\frac{- 18 \cdot x^{5}}{y^{2}})}^{0}$

Step 4

Move the negative in front of the fraction.

${(- \frac{18 \cdot x^{5}}{y^{2}})}^{0}$

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 $- \frac{18 x^{5}}{y^{2}}$ .

${(- 1)}^{0} {(\frac{18 x^{5}}{y^{2}})}^{0}$

Step 5.2

Apply the product rule to $\frac{18 x^{5}}{y^{2}}$ .

${(- 1)}^{0} \frac{{(18 x^{5})}^{0}}{{(y^{2})}^{0}}$

Step 5.3

Apply the product rule to $18 x^{5}$ .

${(- 1)}^{0} \frac{18^{0} {(x^{5})}^{0}}{{(y^{2})}^{0}}$

Step 6

Simplify the expression.

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Step 6.1

Anything raised to $0$ is $1$ .

$1 \frac{18^{0} {(x^{5})}^{0}}{{(y^{2})}^{0}}$

Step 6.2

Multiply $\frac{18^{0} {(x^{5})}^{0}}{{(y^{2})}^{0}}$ by $1$ .

$\frac{18^{0} {(x^{5})}^{0}}{{(y^{2})}^{0}}$

Step 7

Simplify the numerator.

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Step 7.1

Anything raised to $0$ is $1$ .

$\frac{1 {(x^{5})}^{0}}{{(y^{2})}^{0}}$

Step 7.2

Multiply the exponents in ${(x^{5})}^{0}$ .

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Step 7.2.1

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

$\frac{1 x^{5 \cdot 0}}{{(y^{2})}^{0}}$

Step 7.2.2

Multiply $5$ by $0$ .

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

Step 7.3

Anything raised to $0$ is $1$ .

$\frac{1 \cdot 1}{{(y^{2})}^{0}}$

Step 7.4

Multiply $1$ by $1$ .

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

Step 8

Simplify the denominator.

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Step 8.1

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

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Step 8.1.1

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

$\frac{1}{y^{2 \cdot 0}}$

Step 8.1.2

Multiply $2$ by $0$ .

$\frac{1}{y^{0}}$

Step 8.2

Anything raised to $0$ is $1$ .

$\frac{1}{1}$

Step 9

Divide $1$ by $1$ .

$1$