Pre-Algebra Examples

${(81 x^{4})}^{\frac{1}{2}}$

Step 1

Simplify and reorder the polynomial.

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Step 1.1

Simplify the expression.

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Step 1.1.1

Apply the product rule to $81 x^{4}$ .

$81^{\frac{1}{2}} {(x^{4})}^{\frac{1}{2}}$

Step 1.1.2

Rewrite $81$ as $9^{2}$ .

${(9^{2})}^{\frac{1}{2}} {(x^{4})}^{\frac{1}{2}}$

Step 1.1.3

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

$9^{2 (\frac{1}{2})} {(x^{4})}^{\frac{1}{2}}$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Cancel the common factor.

$9^{2 (\frac{1}{2})} {(x^{4})}^{\frac{1}{2}}$

Step 1.2.2

Rewrite the expression.

$9^{1} {(x^{4})}^{\frac{1}{2}}$

Step 1.3

Simplify the expression.

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Step 1.3.1

Evaluate the exponent.

$9 {(x^{4})}^{\frac{1}{2}}$

Step 1.3.2

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

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Step 1.3.2.1

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

$9 x^{4 (\frac{1}{2})}$

Step 1.3.2.2

Cancel the common factor of $2$ .

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Step 1.3.2.2.1

Factor $2$ out of $4$ .

$9 x^{2 (2) \frac{1}{2}}$

Step 1.3.2.2.2

Cancel the common factor.

$9 x^{2 \cdot 2 \frac{1}{2}}$

Step 1.3.2.2.3

Rewrite the expression.

$9 x^{2}$

Step 2

The largest exponent is the degree of the polynomial.

$2$