Algebra Examples

$3 \sqrt{5 a} \cdot - 3 \sqrt{20 a^{3}}$

Step 1

Rewrite $20 a^{3}$ as ${(2 a)}^{2} \cdot (5 a)$ .

Tap for more steps...

Step 1.1

Factor $4$ out of $20$ .

$3 \sqrt{5 a} \cdot (- 3 \sqrt{4 (5) a^{3}})$

Step 1.2

Rewrite $4$ as $2^{2}$ .

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

Step 1.3

Factor out $a^{2}$ .

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

Step 1.4

Move $5$ .

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

Step 1.5

Rewrite $2^{2} a^{2}$ as ${(2 a)}^{2}$ .

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

Step 1.6

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$3 \sqrt{5 a} \cdot (- 3 (2 a \sqrt{5 a}))$

Step 3

Multiply $2$ by $- 3$ .

$3 \sqrt{5 a} \cdot (- 6 (a \sqrt{5 a}))$

Step 4

Multiply $3 \sqrt{5 a} (- 6 a \sqrt{5 a})$ .

Tap for more steps...

Step 4.1

Multiply $- 6$ by $3$ .

$- 18 \sqrt{5 a} (a \sqrt{5 a})$

Step 4.2

Raise $\sqrt{5 a}$ to the power of $1$ .

$- 18 (a ({\sqrt{5 a}}^{1} \sqrt{5 a}))$

Step 4.3

Raise $\sqrt{5 a}$ to the power of $1$ .

$- 18 (a ({\sqrt{5 a}}^{1} {\sqrt{5 a}}^{1}))$

Step 4.4

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

$- 18 (a {\sqrt{5 a}}^{1 + 1})$

Step 4.5

Add $1$ and $1$ .

$- 18 (a {\sqrt{5 a}}^{2})$

Step 5

Rewrite ${\sqrt{5 a}}^{2}$ as $5 a$ .

Tap for more steps...

Step 5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 a}$ as ${(5 a)}^{\frac{1}{2}}$ .

$- 18 (a {({(5 a)}^{\frac{1}{2}})}^{2})$

Step 5.2

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

$- 18 (a {(5 a)}^{\frac{1}{2} \cdot 2})$

Step 5.3

Combine $\frac{1}{2}$ and $2$ .

$- 18 (a {(5 a)}^{\frac{2}{2}})$

Step 5.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 5.4.1

Cancel the common factor.

$- 18 (a {(5 a)}^{\frac{2}{2}})$

Step 5.4.2

Rewrite the expression.

$- 18 (a {(5 a)}^{1})$

Step 5.5

Simplify.

$- 18 (a (5 a))$

Step 6

Multiply $a$ by $a$ by adding the exponents.

Tap for more steps...

Step 6.1

Move $a$ .

$- 18 (a \cdot a \cdot 5)$

Step 6.2

Multiply $a$ by $a$ .

$- 18 (a^{2} \cdot 5)$

Step 7

Move $5$ to the left of $a^{2}$ .

$- 18 (5 \cdot a^{2})$

Step 8

Multiply $5$ by $- 18$ .

$- 90 a^{2}$