Algebra Examples

$5 a \sqrt[3]{125 a^{6}}$

Step 1

Rewrite $125 a^{6}$ as ${(5 a^{2})}^{3}$ .

$5 a \sqrt[3]{{(5 a^{2})}^{3}}$

Step 2

Pull terms out from under the radical, assuming real numbers.

$5 a (5 a^{2})$

Step 3

Rewrite using the commutative property of multiplication.

$5 \cdot 5 a \cdot a^{2}$

Step 4

Multiply $a$ by $a^{2}$ by adding the exponents.

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Step 4.1

Move $a^{2}$ .

$5 \cdot 5 (a^{2} a)$

Step 4.2

Multiply $a^{2}$ by $a$ .

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Step 4.2.1

Raise $a$ to the power of $1$ .

$5 \cdot 5 (a^{2} a^{1})$

Step 4.2.2

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

$5 \cdot 5 a^{2 + 1}$

Step 4.3

Add $2$ and $1$ .

$5 \cdot 5 a^{3}$

Step 5

Multiply $5$ by $5$ .

$25 a^{3}$