Basic Math Examples

$\sqrt{w} \cdot \sqrt{w z^{2}}$

Step 1

Reorder $w$ and $z^{2}$ .

$\sqrt{w} \cdot \sqrt{z^{2} w}$

Step 2

Pull terms out from under the radical.

$\sqrt{w} \cdot (z \sqrt{w})$

Step 3

Multiply $\sqrt{w} (z \sqrt{w})$ .

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Step 3.1

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

$z ({\sqrt{w}}^{1} \sqrt{w})$

Step 3.2

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

$z ({\sqrt{w}}^{1} {\sqrt{w}}^{1})$

Step 3.3

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

$z {\sqrt{w}}^{1 + 1}$

Step 3.4

Add $1$ and $1$ .

$z {\sqrt{w}}^{2}$

Step 4

Rewrite ${\sqrt{w}}^{2}$ as $w$ .

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Step 4.1

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

$z {(w^{\frac{1}{2}})}^{2}$

Step 4.2

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

$z w^{\frac{1}{2} \cdot 2}$

Step 4.3

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

$z w^{\frac{2}{2}}$

Step 4.4

Cancel the common factor of $2$ .

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Step 4.4.1

Cancel the common factor.

$z w^{\frac{2}{2}}$

Step 4.4.2

Rewrite the expression.

$z w^{1}$

Step 4.5

Simplify.

$z w$