Algebra Examples

${(c^{3})}^{2} {(- 3 c^{5})}^{2}$

Step 1

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

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Step 1.1

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

$c^{3 \cdot 2} {(- 3 c^{5})}^{2}$

Step 1.2

Multiply $3$ by $2$ .

$c^{6} {(- 3 c^{5})}^{2}$

Step 2

Apply the product rule to $- 3 c^{5}$ .

$c^{6} ({(- 3)}^{2} {(c^{5})}^{2})$

Step 3

Rewrite using the commutative property of multiplication.

${(- 3)}^{2} c^{6} {(c^{5})}^{2}$

Step 4

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

$9 c^{6} {(c^{5})}^{2}$

Step 5

Multiply the exponents in ${(c^{5})}^{2}$ .

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Step 5.1

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

$9 c^{6} c^{5 \cdot 2}$

Step 5.2

Multiply $5$ by $2$ .

$9 c^{6} c^{10}$

Step 6

Multiply $c^{6}$ by $c^{10}$ by adding the exponents.

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Step 6.1

Move $c^{10}$ .

$9 (c^{10} c^{6})$

Step 6.2

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

$9 c^{10 + 6}$

Step 6.3

Add $10$ and $6$ .

$9 c^{16}$