Algebra Examples

$2 z \sqrt{100 x^{7} z^{4}}$

Step 1

Rewrite $100 x^{7} z^{4}$ as ${(10 x^{3} z^{2})}^{2} x$ .

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Step 1.1

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

$2 z \sqrt{10^{2} x^{7} z^{4}}$

Step 1.2

Factor out $x^{6}$ .

$2 z \sqrt{10^{2} (x^{6} x) z^{4}}$

Step 1.3

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

$2 z \sqrt{10^{2} ({(x^{3})}^{2} x) z^{4}}$

Step 1.4

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

$2 z \sqrt{10^{2} ({(x^{3})}^{2} x) {(z^{2})}^{2}}$

Step 1.5

Move $x$ .

$2 z \sqrt{10^{2} ({(x^{3})}^{2}) {(z^{2})}^{2} x}$

Step 1.6

Rewrite $10^{2} ({(x^{3})}^{2}) {(z^{2})}^{2}$ as ${(10 x^{3} z^{2})}^{2}$ .

$2 z \sqrt{{(10 x^{3} z^{2})}^{2} x}$

Step 2

Pull terms out from under the radical.

$2 z (| 10 x^{3} z^{2} | \sqrt{x})$

Step 3

Remove non-negative terms from the absolute value.

$2 z (10 z^{2} | x^{3} | \sqrt{x})$

Step 4

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

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Step 4.1

Move $z^{2}$ .

$2 (z^{2} z) (10 | x^{3} | \sqrt{x})$

Step 4.2

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

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Step 4.2.1

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

$2 (z^{2} z^{1}) (10 | x^{3} | \sqrt{x})$

Step 4.2.2

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

$2 z^{2 + 1} (10 | x^{3} | \sqrt{x})$

Step 4.3

Add $2$ and $1$ .

$2 z^{3} (10 | x^{3} | \sqrt{x})$

Step 5

Multiply $10$ by $2$ .

$20 z^{3} | x^{3} | \sqrt{x}$