Algebra Examples

${(m^{2} n^{- 5})}^{0} m^{- 7}$

Step 1

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

${(m^{2} \frac{1}{n^{5}})}^{0} m^{- 7}$

Step 2

Combine fractions.

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Step 2.1

Combine $m^{2}$ and $\frac{1}{n^{5}}$ .

${(\frac{m^{2}}{n^{5}})}^{0} m^{- 7}$

Step 2.2

Apply the product rule to $\frac{m^{2}}{n^{5}}$ .

$\frac{{(m^{2})}^{0}}{{(n^{5})}^{0}} m^{- 7}$

Step 3

Simplify the numerator.

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Step 3.1

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

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Step 3.1.1

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

$\frac{m^{2 \cdot 0}}{{(n^{5})}^{0}} m^{- 7}$

Step 3.1.2

Multiply $2$ by $0$ .

$\frac{m^{0}}{{(n^{5})}^{0}} m^{- 7}$

Step 3.2

Anything raised to $0$ is $1$ .

$\frac{1}{{(n^{5})}^{0}} m^{- 7}$

Step 4

Simplify the denominator.

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Step 4.1

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

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Step 4.1.1

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

$\frac{1}{n^{5 \cdot 0}} m^{- 7}$

Step 4.1.2

Multiply $5$ by $0$ .

$\frac{1}{n^{0}} m^{- 7}$

Step 4.2

Anything raised to $0$ is $1$ .

$\frac{1}{1} m^{- 7}$

Step 5

Simplify the expression.

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Step 5.1

Divide $1$ by $1$ .

$1 m^{- 7}$

Step 5.2

Multiply $m^{- 7}$ by $1$ .

$m^{- 7}$

Step 6

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

$\frac{1}{m^{7}}$