Basic Math Examples

${(\frac{m^{- 3} m^{- 7}}{{(m^{- 4})}^{- 3}})}^{5}$

Step 1

Multiply $m^{- 3}$ by $m^{- 7}$ by adding the exponents.

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Step 1.1

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

${(\frac{m^{- 3 - 7}}{{(m^{- 4})}^{- 3}})}^{5}$

Step 1.2

Subtract $7$ from $- 3$ .

${(\frac{m^{- 10}}{{(m^{- 4})}^{- 3}})}^{5}$

Step 2

Simplify the expression.

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Step 2.1

Move $m^{- 10}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{1}{{(m^{- 4})}^{- 3} m^{10}})}^{5}$

Step 2.2

Move ${(m^{- 4})}^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{{(m^{- 4})}^{3}}{m^{10}})}^{5}$

Step 3

Simplify the numerator.

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Step 3.1

Multiply the exponents in ${(m^{- 4})}^{3}$ .

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Step 3.1.1

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

${(\frac{m^{- 4 \cdot 3}}{m^{10}})}^{5}$

Step 3.1.2

Multiply $- 4$ by $3$ .

${(\frac{m^{- 12}}{m^{10}})}^{5}$

Step 3.2

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

${(\frac{\frac{1}{m^{12}}}{m^{10}})}^{5}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

${(\frac{1}{m^{12}} \cdot \frac{1}{m^{10}})}^{5}$

Step 5

Combine.

${(\frac{1 \cdot 1}{m^{12} m^{10}})}^{5}$

Step 6

Multiply $m^{12}$ by $m^{10}$ by adding the exponents.

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Step 6.1

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

${(\frac{1 \cdot 1}{m^{12 + 10}})}^{5}$

Step 6.2

Add $12$ and $10$ .

${(\frac{1 \cdot 1}{m^{22}})}^{5}$

Step 7

Multiply $1$ by $1$ .

${(\frac{1}{m^{22}})}^{5}$

Step 8

Apply the product rule to $\frac{1}{m^{22}}$ .

$\frac{1^{5}}{{(m^{22})}^{5}}$

Step 9

One to any power is one.

$\frac{1}{{(m^{22})}^{5}}$

Step 10

Multiply the exponents in ${(m^{22})}^{5}$ .

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Step 10.1

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

$\frac{1}{m^{22 \cdot 5}}$

Step 10.2

Multiply $22$ by $5$ .

$\frac{1}{m^{110}}$