Basic Math Examples

${(- 2 a^{4} b^{3})}^{7} {(a^{2} b)}^{5}$

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 $- 2 a^{4} b^{3}$ .

${(- 2 a^{4})}^{7} {(b^{3})}^{7} {(a^{2} b)}^{5}$

Step 1.2

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

${(- 2)}^{7} {(a^{4})}^{7} {(b^{3})}^{7} {(a^{2} b)}^{5}$

Step 2

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

$- 128 {(a^{4})}^{7} {(b^{3})}^{7} {(a^{2} b)}^{5}$

Step 3

Multiply the exponents in ${(a^{4})}^{7}$ .

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Step 3.1

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

$- 128 a^{4 \cdot 7} {(b^{3})}^{7} {(a^{2} b)}^{5}$

Step 3.2

Multiply $4$ by $7$ .

$- 128 a^{28} {(b^{3})}^{7} {(a^{2} b)}^{5}$

Step 4

Multiply the exponents in ${(b^{3})}^{7}$ .

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Step 4.1

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

$- 128 a^{28} b^{3 \cdot 7} {(a^{2} b)}^{5}$

Step 4.2

Multiply $3$ by $7$ .

$- 128 a^{28} b^{21} {(a^{2} b)}^{5}$

Step 5

Apply the product rule to $a^{2} b$ .

$- 128 a^{28} b^{21} ({(a^{2})}^{5} b^{5})$

Step 6

Multiply $b^{21}$ by $b^{5}$ by adding the exponents.

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Step 6.1

Move $b^{5}$ .

$- 128 a^{28} (b^{5} b^{21}) {(a^{2})}^{5}$

Step 6.2

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

$- 128 a^{28} b^{5 + 21} {(a^{2})}^{5}$

Step 6.3

Add $5$ and $21$ .

$- 128 a^{28} b^{26} {(a^{2})}^{5}$

Step 7

Multiply the exponents in ${(a^{2})}^{5}$ .

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Step 7.1

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

$- 128 a^{28} b^{26} a^{2 \cdot 5}$

Step 7.2

Multiply $2$ by $5$ .

$- 128 a^{28} b^{26} a^{10}$

Step 8

Multiply $a^{28}$ by $a^{10}$ by adding the exponents.

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Step 8.1

Move $a^{10}$ .

$- 128 (a^{10} a^{28}) b^{26}$

Step 8.2

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

$- 128 a^{10 + 28} b^{26}$

Step 8.3

Add $10$ and $28$ .

$- 128 a^{38} b^{26}$