Basic Math Examples

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

Step 1

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

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

Step 2

Multiply the exponents in ${(a^{4})}^{5}$ .

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Step 2.1

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

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

Step 2.2

Multiply $4$ by $5$ .

$- 3 a^{3} b (a^{20} {(b^{4})}^{5})$

Step 3

Multiply $a^{3}$ by $a^{20}$ by adding the exponents.

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Step 3.1

Move $a^{20}$ .

$- 3 (a^{20} a^{3}) b {(b^{4})}^{5}$

Step 3.2

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

$- 3 a^{20 + 3} b {(b^{4})}^{5}$

Step 3.3

Add $20$ and $3$ .

$- 3 a^{23} b {(b^{4})}^{5}$

Step 4

Multiply the exponents in ${(b^{4})}^{5}$ .

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Step 4.1

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

$- 3 a^{23} b \cdot b^{4 \cdot 5}$

Step 4.2

Multiply $4$ by $5$ .

$- 3 a^{23} b \cdot b^{20}$

Step 5

Multiply $b$ by $b^{20}$ by adding the exponents.

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Step 5.1

Move $b^{20}$ .

$- 3 a^{23} (b^{20} b)$

Step 5.2

Multiply $b^{20}$ by $b$ .

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Step 5.2.1

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

$- 3 a^{23} (b^{20} b^{1})$

Step 5.2.2

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

$- 3 a^{23} b^{20 + 1}$

Step 5.3

Add $20$ and $1$ .

$- 3 a^{23} b^{21}$