Basic Math Examples

$(\sqrt[4]{y^{2}}) \cdot (\sqrt[4]{y^{2}})$

Step 1

Rewrite $\sqrt[4]{y^{2}}$ as $\sqrt{\sqrt{y^{2}}}$ .

$\sqrt{\sqrt{y^{2}}} \cdot \sqrt[4]{y^{2}}$

Step 2

Pull terms out from under the radical, assuming positive real numbers.

$\sqrt{y} \cdot \sqrt[4]{y^{2}}$

Step 3

Rewrite $\sqrt[4]{y^{2}}$ as $\sqrt{\sqrt{y^{2}}}$ .

$\sqrt{y} \cdot \sqrt{\sqrt{y^{2}}}$

Step 4

Pull terms out from under the radical, assuming positive real numbers.

$\sqrt{y} \cdot \sqrt{y}$

Step 5

Multiply $\sqrt{y} \sqrt{y}$ .

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Step 5.1

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

${\sqrt{y}}^{1} \sqrt{y}$

Step 5.2

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

${\sqrt{y}}^{1} {\sqrt{y}}^{1}$

Step 5.3

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

${\sqrt{y}}^{1 + 1}$

Step 5.4

Add $1$ and $1$ .

${\sqrt{y}}^{2}$

Step 6

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

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Step 6.1

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

${(y^{\frac{1}{2}})}^{2}$

Step 6.2

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

$y^{\frac{1}{2} \cdot 2}$

Step 6.3

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

$y^{\frac{2}{2}}$

Step 6.4

Cancel the common factor of $2$ .

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Step 6.4.1

Cancel the common factor.

$y^{\frac{2}{2}}$

Step 6.4.2

Rewrite the expression.

$y^{1}$

Step 6.5

Simplify.

$y$