Basic Math Examples

${(5 k)}^{2} {(2 k)}^{3}$

Step 1

Apply the product rule to $5 k$ .

$5^{2} k^{2} {(2 k)}^{3}$

Step 2

Raise $5$ to the power of $2$ .

$25 k^{2} {(2 k)}^{3}$

Step 3

Apply the product rule to $2 k$ .

$25 k^{2} (2^{3} k^{3})$

Step 4

Rewrite using the commutative property of multiplication.

$25 \cdot 2^{3} k^{2} k^{3}$

Step 5

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

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Step 5.1

Move $k^{3}$ .

$25 \cdot 2^{3} (k^{3} k^{2})$

Step 5.2

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

$25 \cdot 2^{3} k^{3 + 2}$

Step 5.3

Add $3$ and $2$ .

$25 \cdot 2^{3} k^{5}$

Step 6

Raise $2$ to the power of $3$ .

$25 \cdot 8 k^{5}$

Step 7

Multiply $25$ by $8$ .

$200 k^{5}$