Algebra Examples

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

Step 1

Apply the product rule to $x^{2} y^{\frac{1}{2}}$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Multiply $2$ by $4$ .

$x^{8} {(y^{\frac{1}{2}})}^{4}$

Step 3

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

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Step 3.1

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

$x^{8} y^{\frac{1}{2} \cdot 4}$

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Factor $2$ out of $4$ .

$x^{8} y^{\frac{1}{2} \cdot (2 (2))}$

Step 3.2.2

Cancel the common factor.

$x^{8} y^{\frac{1}{2} \cdot (2 \cdot 2)}$

Step 3.2.3

Rewrite the expression.

$x^{8} y^{2}$