Algebra Examples

${(x^{4} y)}^{\frac{1}{2}} + {(x y^{\frac{1}{4}})}^{2}$

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $x^{4} y$ .

${(x^{4})}^{\frac{1}{2}} y^{\frac{1}{2}} + {(x y^{\frac{1}{4}})}^{2}$

Step 1.2

Multiply the exponents in ${(x^{4})}^{\frac{1}{2}}$ .

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Step 1.2.1

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

$x^{4 (\frac{1}{2})} y^{\frac{1}{2}} + {(x y^{\frac{1}{4}})}^{2}$

Step 1.2.2

Cancel the common factor of $2$ .

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Step 1.2.2.1

Factor $2$ out of $4$ .

$x^{2 (2) \frac{1}{2}} y^{\frac{1}{2}} + {(x y^{\frac{1}{4}})}^{2}$

Step 1.2.2.2

Cancel the common factor.

$x^{2 \cdot 2 \frac{1}{2}} y^{\frac{1}{2}} + {(x y^{\frac{1}{4}})}^{2}$

Step 1.2.2.3

Rewrite the expression.

$x^{2} y^{\frac{1}{2}} + {(x y^{\frac{1}{4}})}^{2}$

Step 1.3

Apply the product rule to $x y^{\frac{1}{4}}$ .

$x^{2} y^{\frac{1}{2}} + x^{2} {(y^{\frac{1}{4}})}^{2}$

Step 1.4

Multiply the exponents in ${(y^{\frac{1}{4}})}^{2}$ .

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Step 1.4.1

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

$x^{2} y^{\frac{1}{2}} + x^{2} y^{\frac{1}{4} \cdot 2}$

Step 1.4.2

Cancel the common factor of $2$ .

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Step 1.4.2.1

Factor $2$ out of $4$ .

$x^{2} y^{\frac{1}{2}} + x^{2} y^{\frac{1}{2 (2)} \cdot 2}$

Step 1.4.2.2

Cancel the common factor.

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

Step 1.4.2.3

Rewrite the expression.

$x^{2} y^{\frac{1}{2}} + x^{2} y^{\frac{1}{2}}$

Step 2

Add $x^{2} y^{\frac{1}{2}}$ and $x^{2} y^{\frac{1}{2}}$ .

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