Basic Math Examples

${(3 a b)}^{3} {(4 a^{3} b)}^{2}$

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 $3 a b$ .

${(3 a)}^{3} b^{3} {(4 a^{3} b)}^{2}$

Step 1.2

Apply the product rule to $3 a$ .

$3^{3} a^{3} b^{3} {(4 a^{3} b)}^{2}$

Step 2

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

$27 a^{3} b^{3} {(4 a^{3} b)}^{2}$

Step 3

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

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Step 3.1

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

$27 a^{3} b^{3} ({(4 a^{3})}^{2} b^{2})$

Step 3.2

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

$27 a^{3} b^{3} (4^{2} {(a^{3})}^{2} b^{2})$

Step 4

Multiply $b^{3}$ by $b^{2}$ by adding the exponents.

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Step 4.1

Move $b^{2}$ .

$27 a^{3} (b^{2} b^{3}) (4^{2} {(a^{3})}^{2})$

Step 4.2

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

$27 a^{3} b^{2 + 3} (4^{2} {(a^{3})}^{2})$

Step 4.3

Add $2$ and $3$ .

$27 a^{3} b^{5} (4^{2} {(a^{3})}^{2})$

Step 5

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

$27 a^{3} b^{5} (16 {(a^{3})}^{2})$

Step 6

Multiply the exponents in ${(a^{3})}^{2}$ .

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Step 6.1

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

$27 a^{3} b^{5} (16 a^{3 \cdot 2})$

Step 6.2

Multiply $3$ by $2$ .

$27 a^{3} b^{5} (16 a^{6})$

Step 7

Multiply $a^{3}$ by $a^{6}$ by adding the exponents.

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Step 7.1

Move $a^{6}$ .

$27 (a^{6} a^{3}) b^{5} \cdot 16$

Step 7.2

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

$27 a^{6 + 3} b^{5} \cdot 16$

Step 7.3

Add $6$ and $3$ .

$27 a^{9} b^{5} \cdot 16$

Step 8

Multiply $16$ by $27$ .

$432 a^{9} b^{5}$