Algebra Examples

${(25 x^{4})}^{\frac{1}{2}}$

Step 1

Simplify the expression.

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Step 1.1

Apply the product rule to $25 x^{4}$ .

$25^{\frac{1}{2}} {(x^{4})}^{\frac{1}{2}}$

Step 1.2

Rewrite $25$ as $5^{2}$ .

${(5^{2})}^{\frac{1}{2}} {(x^{4})}^{\frac{1}{2}}$

Step 1.3

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

$5^{2 (\frac{1}{2})} {(x^{4})}^{\frac{1}{2}}$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Cancel the common factor.

$5^{2 (\frac{1}{2})} {(x^{4})}^{\frac{1}{2}}$

Step 2.2

Rewrite the expression.

$5^{1} {(x^{4})}^{\frac{1}{2}}$

Step 3

Evaluate the exponent.

$5 {(x^{4})}^{\frac{1}{2}}$

Step 4

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

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Step 4.1

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

$5 x^{4 (\frac{1}{2})}$

Step 4.2

Cancel the common factor of $2$ .

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Step 4.2.1

Factor $2$ out of $4$ .

$5 x^{2 (2) \frac{1}{2}}$

Step 4.2.2

Cancel the common factor.

$5 x^{2 \cdot 2 \frac{1}{2}}$

Step 4.2.3

Rewrite the expression.

$5 x^{2}$