Basic Math Examples

${(2 m^{2} n^{- 2})}^{- 2} \cdot (2 (n m^{4}))$

Step 1

Rewrite using the commutative property of multiplication.

$2 {(2 m^{2} n^{- 2})}^{- 2} n m^{4}$

Step 2

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

$2 {(2 m^{2} \frac{1}{n^{2}})}^{- 2} n m^{4}$

Step 3

Multiply $2 m^{2} \frac{1}{n^{2}}$ .

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Step 3.1

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

$2 {(m^{2} \frac{2}{n^{2}})}^{- 2} n m^{4}$

Step 3.2

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

$2 {(\frac{m^{2} \cdot 2}{n^{2}})}^{- 2} n m^{4}$

Step 4

Move $2$ to the left of $m^{2}$ .

$2 {(\frac{2 \cdot m^{2}}{n^{2}})}^{- 2} n m^{4}$

Step 5

Change the sign of the exponent by rewriting the base as its reciprocal.

$2 {(\frac{n^{2}}{2 m^{2}})}^{2} n m^{4}$

Step 6

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

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Step 6.1

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

$2 \frac{{(n^{2})}^{2}}{{(2 m^{2})}^{2}} n m^{4}$

Step 6.2

Apply the product rule to $2 m^{2}$ .

$2 \frac{{(n^{2})}^{2}}{2^{2} {(m^{2})}^{2}} n m^{4}$

Step 7

Cancel the common factor of $2$ .

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Step 7.1

Factor $2$ out of $2^{2} {(m^{2})}^{2}$ .

$2 \frac{{(n^{2})}^{2}}{2 (2 {(m^{2})}^{2})} n m^{4}$

Step 7.2

Cancel the common factor.

$2 \frac{{(n^{2})}^{2}}{2 (2 {(m^{2})}^{2})} n m^{4}$

Step 7.3

Rewrite the expression.

$\frac{{(n^{2})}^{2}}{2 {(m^{2})}^{2}} n m^{4}$

Step 8

Apply basic rules of exponents.

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Step 8.1

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

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Step 8.1.1

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

$\frac{n^{2 \cdot 2}}{2 {(m^{2})}^{2}} n m^{4}$

Step 8.1.2

Multiply $2$ by $2$ .

$\frac{n^{4}}{2 {(m^{2})}^{2}} n m^{4}$

Step 8.2

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

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Step 8.2.1

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

$\frac{n^{4}}{2 m^{2 \cdot 2}} n m^{4}$

Step 8.2.2

Multiply $2$ by $2$ .

$\frac{n^{4}}{2 m^{4}} n m^{4}$

Step 9

Multiply $\frac{n^{4}}{2 m^{4}} n$ .

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Step 9.1

Combine $\frac{n^{4}}{2 m^{4}}$ and $n$ .

$\frac{n^{4} n}{2 m^{4}} m^{4}$

Step 9.2

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

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Step 9.2.1

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

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Step 9.2.1.1

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

$\frac{n^{4} n^{1}}{2 m^{4}} m^{4}$

Step 9.2.1.2

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

$\frac{n^{4 + 1}}{2 m^{4}} m^{4}$

Step 9.2.2

Add $4$ and $1$ .

$\frac{n^{5}}{2 m^{4}} m^{4}$

Step 10

Cancel the common factor of $m^{4}$ .

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Step 10.1

Factor $m^{4}$ out of $2 m^{4}$ .

$\frac{n^{5}}{m^{4} \cdot 2} m^{4}$

Step 10.2

Cancel the common factor.

$\frac{n^{5}}{m^{4} \cdot 2} m^{4}$

Step 10.3

Rewrite the expression.

$\frac{n^{5}}{2}$