Basic Math Examples

${(2 r^{2})}^{2} \cdot {(2 r)}^{2}$

Step 1

Apply the product rule to $2 r^{2}$ .

$2^{2} {(r^{2})}^{2} \cdot {(2 r)}^{2}$

Step 2

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

$4 {(r^{2})}^{2} \cdot {(2 r)}^{2}$

Step 3

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

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Step 3.1

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

$4 r^{2 \cdot 2} \cdot {(2 r)}^{2}$

Step 3.2

Multiply $2$ by $2$ .

$4 r^{4} \cdot {(2 r)}^{2}$

Step 4

Apply the product rule to $2 r$ .

$4 r^{4} \cdot (2^{2} r^{2})$

Step 5

Rewrite using the commutative property of multiplication.

$4 \cdot 2^{2} r^{4} r^{2}$

Step 6

Multiply $r^{4}$ by $r^{2}$ by adding the exponents.

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Step 6.1

Move $r^{2}$ .

$4 \cdot 2^{2} (r^{2} r^{4})$

Step 6.2

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

$4 \cdot 2^{2} r^{2 + 4}$

Step 6.3

Add $2$ and $4$ .

$4 \cdot 2^{2} r^{6}$

Step 7

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

$4 \cdot 4 r^{6}$

Step 8

Multiply $4$ by $4$ .

$16 r^{6}$