Algebra Examples

${(x^{\frac{1}{2}})}^{4} \sqrt{x^{6}}$

Step 1

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

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Step 1.1

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

$x^{\frac{1}{2} \cdot 4} \sqrt{x^{6}}$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Factor $2$ out of $4$ .

$x^{\frac{1}{2} \cdot (2 (2))} \sqrt{x^{6}}$

Step 1.2.2

Cancel the common factor.

$x^{\frac{1}{2} \cdot (2 \cdot 2)} \sqrt{x^{6}}$

Step 1.2.3

Rewrite the expression.

$x^{2} \sqrt{x^{6}}$

Step 2

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

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

Step 3

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

$x^{2} x^{3}$

Step 4

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

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Step 4.1

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

$x^{2 + 3}$

Step 4.2

Add $2$ and $3$ .

$x^{5}$