Basic Math Examples

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

Step 1

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

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

Step 2

Factor.

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Step 2.1

Apply the product rule to $2 a^{3} b^{4}$ .

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

Step 2.2

Remove unnecessary parentheses.

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

Step 3

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

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

Step 4

Factor.

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Step 4.1

Apply the product rule to $2 a^{3}$ .

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

Step 4.2

Remove unnecessary parentheses.

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

Step 5

Combine exponents.

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Step 5.1

Rewrite $4$ as $2^{2}$ .

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

Step 5.2

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

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Step 5.2.1

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

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

Step 5.2.2

Multiply $2$ by $2$ .

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

Step 5.3

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

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

Step 5.4

Add $4$ and $4$ .

$2^{8} {(a^{2})}^{2} b^{2} {(a^{3})}^{4} {(b^{4})}^{4}$