Algebra Examples

$2 a b^{2} \sqrt{\frac{200 a^{2} b^{5} c^{11}}{c^{11}}}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Reduce the expression $\frac{200 a^{2} b^{5} c^{11}}{c^{11}}$ by cancelling the common factors.

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Step 1.1.1

Cancel the common factor.

$2 a b^{2} \sqrt{\frac{200 a^{2} b^{5} c^{11}}{c^{11}}}$

Step 1.1.2

Rewrite the expression.

$2 a b^{2} \sqrt{\frac{200 a^{2} b^{5}}{1}}$

Step 1.2

Divide $200 a^{2} b^{5}$ by $1$ .

$2 a b^{2} \sqrt{200 a^{2} b^{5}}$

Step 2

Rewrite $200 a^{2} b^{5}$ as ${(10 a b^{2})}^{2} \cdot (2 b)$ .

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Step 2.1

Factor $100$ out of $200$ .

$2 a b^{2} \sqrt{100 (2) a^{2} b^{5}}$

Step 2.2

Rewrite $100$ as $10^{2}$ .

$2 a b^{2} \sqrt{10^{2} \cdot 2 a^{2} b^{5}}$

Step 2.3

Factor out $b^{4}$ .

$2 a b^{2} \sqrt{10^{2} \cdot 2 a^{2} (b^{4} b)}$

Step 2.4

Rewrite $b^{4}$ as ${(b^{2})}^{2}$ .

$2 a b^{2} \sqrt{10^{2} \cdot 2 a^{2} ({(b^{2})}^{2} b)}$

Step 2.5

Move $2$ .

$2 a b^{2} \sqrt{10^{2} a^{2} {(b^{2})}^{2} \cdot 2 b}$

Step 2.6

Rewrite $10^{2} a^{2} {(b^{2})}^{2}$ as ${(10 a b^{2})}^{2}$ .

$2 a b^{2} \sqrt{{(10 a b^{2})}^{2} \cdot 2 b}$

Step 2.7

Add parentheses.

$2 a b^{2} \sqrt{{(10 a b^{2})}^{2} \cdot (2 b)}$

Step 3

Pull terms out from under the radical.

$2 a b^{2} (10 a b^{2} \sqrt{2 b})$

Step 4

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

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Step 4.1

Move $a$ .

$2 (a \cdot a) b^{2} (10 b^{2} \sqrt{2 b})$

Step 4.2

Multiply $a$ by $a$ .

$2 a^{2} b^{2} (10 b^{2} \sqrt{2 b})$

Step 5

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

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Step 5.1

Move $b^{2}$ .

$2 a^{2} (b^{2} b^{2}) (10 \sqrt{2 b})$

Step 5.2

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

$2 a^{2} b^{2 + 2} (10 \sqrt{2 b})$

Step 5.3

Add $2$ and $2$ .

$2 a^{2} b^{4} (10 \sqrt{2 b})$

Step 6

Multiply $10$ by $2$ .

$20 a^{2} b^{4} \sqrt{2 b}$