Basic Math Examples

$2 b \sqrt[5]{b^{6}} - 3 \sqrt[5]{32 b^{11}}$

Step 1

Simplify each term.

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Step 1.1

Factor out $b^{5}$ .

$2 b \sqrt[5]{b^{5} b} - 3 \sqrt[5]{32 b^{11}}$

Step 1.2

Pull terms out from under the radical.

$2 b (b \sqrt[5]{b}) - 3 \sqrt[5]{32 b^{11}}$

Step 1.3

Multiply $b$ by $b$ by adding the exponents.

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Step 1.3.1

Move $b$ .

$2 (b \cdot b) \sqrt[5]{b} - 3 \sqrt[5]{32 b^{11}}$

Step 1.3.2

Multiply $b$ by $b$ .

$2 b^{2} \sqrt[5]{b} - 3 \sqrt[5]{32 b^{11}}$

Step 1.4

Rewrite $32 b^{11}$ as ${(2 b^{2})}^{5} b$ .

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Step 1.4.1

Rewrite $32$ as $2^{5}$ .

$2 b^{2} \sqrt[5]{b} - 3 \sqrt[5]{2^{5} b^{11}}$

Step 1.4.2

Factor out $b^{10}$ .

$2 b^{2} \sqrt[5]{b} - 3 \sqrt[5]{2^{5} (b^{10} b)}$

Step 1.4.3

Rewrite $b^{10}$ as ${(b^{2})}^{5}$ .

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

Step 1.4.4

Rewrite $2^{5} {(b^{2})}^{5}$ as ${(2 b^{2})}^{5}$ .

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

Step 1.5

Pull terms out from under the radical.

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

Step 1.6

Multiply $2$ by $- 3$ .

$2 b^{2} \sqrt[5]{b} - 6 b^{2} \sqrt[5]{b}$

Step 2

Subtract $6 b^{2} \sqrt[5]{b}$ from $2 b^{2} \sqrt[5]{b}$ .

$- 4 b^{2} \sqrt[5]{b}$