Algebra Examples

${(2 g h^{4})}^{3} {({(- 2 g^{4} h)}^{3})}^{2}$

Step 1

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

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Step 1.1

Apply the product rule to $2 g h^{4}$ .

${(2 g)}^{3} {(h^{4})}^{3} {({(- 2 g^{4} h)}^{3})}^{2}$

Step 1.2

Apply the product rule to $2 g$ .

$2^{3} g^{3} {(h^{4})}^{3} {({(- 2 g^{4} h)}^{3})}^{2}$

Step 2

Raise $2$ to the power of $3$ .

$8 g^{3} {(h^{4})}^{3} {({(- 2 g^{4} h)}^{3})}^{2}$

Step 3

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

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Step 3.1

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

$8 g^{3} h^{4 \cdot 3} {({(- 2 g^{4} h)}^{3})}^{2}$

Step 3.2

Multiply $4$ by $3$ .

$8 g^{3} h^{12} {({(- 2 g^{4} h)}^{3})}^{2}$

Step 4

Multiply the exponents in ${({(- 2 g^{4} h)}^{3})}^{2}$ .

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Step 4.1

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

$8 g^{3} h^{12} {(- 2 g^{4} h)}^{3 \cdot 2}$

Step 4.2

Multiply $3$ by $2$ .

$8 g^{3} h^{12} {(- 2 g^{4} h)}^{6}$

Step 5

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

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Step 5.1

Apply the product rule to $- 2 g^{4} h$ .

$8 g^{3} h^{12} ({(- 2 g^{4})}^{6} h^{6})$

Step 5.2

Apply the product rule to $- 2 g^{4}$ .

$8 g^{3} h^{12} ({(- 2)}^{6} {(g^{4})}^{6} h^{6})$

Step 6

Multiply $h^{12}$ by $h^{6}$ by adding the exponents.

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Step 6.1

Move $h^{6}$ .

$8 g^{3} (h^{6} h^{12}) ({(- 2)}^{6} {(g^{4})}^{6})$

Step 6.2

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

$8 g^{3} h^{6 + 12} ({(- 2)}^{6} {(g^{4})}^{6})$

Step 6.3

Add $6$ and $12$ .

$8 g^{3} h^{18} ({(- 2)}^{6} {(g^{4})}^{6})$

Step 7

Raise $- 2$ to the power of $6$ .

$8 g^{3} h^{18} (64 {(g^{4})}^{6})$

Step 8

Multiply the exponents in ${(g^{4})}^{6}$ .

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Step 8.1

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

$8 g^{3} h^{18} (64 g^{4 \cdot 6})$

Step 8.2

Multiply $4$ by $6$ .

$8 g^{3} h^{18} (64 g^{24})$

Step 9

Multiply $g^{3}$ by $g^{24}$ by adding the exponents.

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Step 9.1

Move $g^{24}$ .

$8 (g^{24} g^{3}) h^{18} \cdot 64$

Step 9.2

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

$8 g^{24 + 3} h^{18} \cdot 64$

Step 9.3

Add $24$ and $3$ .

$8 g^{27} h^{18} \cdot 64$

Step 10

Multiply $64$ by $8$ .

$512 g^{27} h^{18}$