Algebra Examples

${(- 7 m^{6} n^{4})}^{2} - {(4 m^{3} n^{2})}^{4}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Apply the product rule to $- 7 m^{6} n^{4}$ .

${(- 7 m^{6})}^{2} {(n^{4})}^{2} - {(4 m^{3} n^{2})}^{4}$

Step 1.1.2

Apply the product rule to $- 7 m^{6}$ .

${(- 7)}^{2} {(m^{6})}^{2} {(n^{4})}^{2} - {(4 m^{3} n^{2})}^{4}$

Step 1.2

Raise $- 7$ to the power of $2$ .

$49 {(m^{6})}^{2} {(n^{4})}^{2} - {(4 m^{3} n^{2})}^{4}$

Step 1.3

Multiply the exponents in ${(m^{6})}^{2}$ .

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Step 1.3.1

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

$49 m^{6 \cdot 2} {(n^{4})}^{2} - {(4 m^{3} n^{2})}^{4}$

Step 1.3.2

Multiply $6$ by $2$ .

$49 m^{12} {(n^{4})}^{2} - {(4 m^{3} n^{2})}^{4}$

Step 1.4

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

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Step 1.4.1

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

$49 m^{12} n^{4 \cdot 2} - {(4 m^{3} n^{2})}^{4}$

Step 1.4.2

Multiply $4$ by $2$ .

$49 m^{12} n^{8} - {(4 m^{3} n^{2})}^{4}$

Step 1.5

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

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Step 1.5.1

Apply the product rule to $4 m^{3} n^{2}$ .

$49 m^{12} n^{8} - ({(4 m^{3})}^{4} {(n^{2})}^{4})$

Step 1.5.2

Apply the product rule to $4 m^{3}$ .

$49 m^{12} n^{8} - (4^{4} {(m^{3})}^{4} {(n^{2})}^{4})$

Step 1.6

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

$49 m^{12} n^{8} - (256 {(m^{3})}^{4} {(n^{2})}^{4})$

Step 1.7

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

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Step 1.7.1

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

$49 m^{12} n^{8} - (256 m^{3 \cdot 4} {(n^{2})}^{4})$

Step 1.7.2

Multiply $3$ by $4$ .

$49 m^{12} n^{8} - (256 m^{12} {(n^{2})}^{4})$

Step 1.8

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

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Step 1.8.1

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

$49 m^{12} n^{8} - (256 m^{12} n^{2 \cdot 4})$

Step 1.8.2

Multiply $2$ by $4$ .

$49 m^{12} n^{8} - (256 m^{12} n^{8})$

Step 1.9

Multiply $256$ by $- 1$ .

$49 m^{12} n^{8} - 256 m^{12} n^{8}$

Step 2

Subtract $256 m^{12} n^{8}$ from $49 m^{12} n^{8}$ .

$- 207 m^{12} n^{8}$