Basic Math Examples

$6 d^{2} \cdot {(2 d^{5})}^{4}$

Step 1

Apply the product rule to $2 d^{5}$ .

$6 d^{2} \cdot (2^{4} {(d^{5})}^{4})$

Step 2

Rewrite using the commutative property of multiplication.

$6 \cdot 2^{4} d^{2} {(d^{5})}^{4}$

Step 3

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

$6 \cdot 16 d^{2} {(d^{5})}^{4}$

Step 4

Multiply $6$ by $16$ .

$96 d^{2} {(d^{5})}^{4}$

Step 5

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

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Step 5.1

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

$96 d^{2} d^{5 \cdot 4}$

Step 5.2

Multiply $5$ by $4$ .

$96 d^{2} d^{20}$

Step 6

Multiply $d^{2}$ by $d^{20}$ by adding the exponents.

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Step 6.1

Move $d^{20}$ .

$96 (d^{20} d^{2})$

Step 6.2

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

$96 d^{20 + 2}$

Step 6.3

Add $20$ and $2$ .

$96 d^{22}$