Algebra Examples

${(\frac{2 m^{- 1} n^{4} \cdot 3 m^{6} n^{2}}{4 m^{7} n^{6}})}^{4}$

Step 1

Multiply $m^{- 1}$ by $m^{6}$ by adding the exponents.

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Step 1.1

Move $m^{6}$ .

${(\frac{2 (m^{6} m^{- 1}) n^{4} \cdot (3 n^{2})}{4 m^{7} n^{6}})}^{4}$

Step 1.2

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

${(\frac{2 m^{6 - 1} n^{4} \cdot (3 n^{2})}{4 m^{7} n^{6}})}^{4}$

Step 1.3

Subtract $1$ from $6$ .

${(\frac{2 m^{5} n^{4} \cdot (3 n^{2})}{4 m^{7} n^{6}})}^{4}$

Step 2

Multiply $n^{4}$ by $n^{2}$ by adding the exponents.

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Step 2.1

Move $n^{2}$ .

${(\frac{2 m^{5} (n^{2} n^{4}) \cdot 3}{4 m^{7} n^{6}})}^{4}$

Step 2.2

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

${(\frac{2 m^{5} n^{2 + 4} \cdot 3}{4 m^{7} n^{6}})}^{4}$

Step 2.3

Add $2$ and $4$ .

${(\frac{2 m^{5} n^{6} \cdot 3}{4 m^{7} n^{6}})}^{4}$

Step 3

Cancel the common factor of $2$ and $4$ .

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Step 3.1

Factor $2$ out of $2 m^{5} n^{6} \cdot 3$ .

${(\frac{2 (m^{5} n^{6} \cdot 3)}{4 m^{7} n^{6}})}^{4}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $4 m^{7} n^{6}$ .

${(\frac{2 (m^{5} n^{6} \cdot 3)}{2 (2 m^{7} n^{6})})}^{4}$

Step 3.2.2

Cancel the common factor.

${(\frac{2 (m^{5} n^{6} \cdot 3)}{2 (2 m^{7} n^{6})})}^{4}$

Step 3.2.3

Rewrite the expression.

${(\frac{m^{5} n^{6} \cdot 3}{2 m^{7} n^{6}})}^{4}$

Step 4

Cancel the common factor of $m^{5}$ and $m^{7}$ .

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Step 4.1

Factor $m^{5}$ out of $m^{5} n^{6} \cdot 3$ .

${(\frac{m^{5} (n^{6} \cdot 3)}{2 m^{7} n^{6}})}^{4}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $m^{5}$ out of $2 m^{7} n^{6}$ .

${(\frac{m^{5} (n^{6} \cdot 3)}{m^{5} (2 m^{2} n^{6})})}^{4}$

Step 4.2.2

Cancel the common factor.

${(\frac{m^{5} (n^{6} \cdot 3)}{m^{5} (2 m^{2} n^{6})})}^{4}$

Step 4.2.3

Rewrite the expression.

${(\frac{n^{6} \cdot 3}{2 m^{2} n^{6}})}^{4}$

Step 5

Cancel the common factor of $n^{6}$ .

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Step 5.1

Cancel the common factor.

${(\frac{n^{6} \cdot 3}{2 m^{2} n^{6}})}^{4}$

Step 5.2

Rewrite the expression.

${(\frac{3}{2 m^{2}})}^{4}$

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 $\frac{3}{2 m^{2}}$ .

$\frac{3^{4}}{{(2 m^{2})}^{4}}$

Step 6.2

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

$\frac{3^{4}}{2^{4} {(m^{2})}^{4}}$

Step 7

Raise $3$ to the power of $4$ .

$\frac{81}{2^{4} {(m^{2})}^{4}}$

Step 8

Simplify the denominator.

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Step 8.1

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

$\frac{81}{16 {(m^{2})}^{4}}$

Step 8.2

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

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Step 8.2.1

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

$\frac{81}{16 m^{2 \cdot 4}}$

Step 8.2.2

Multiply $2$ by $4$ .

$\frac{81}{16 m^{8}}$