Basic Math Examples

${(81^{\frac{1}{2}} - 9^{\frac{1}{2}})}^{2}$

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Cancel the common factor.

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

Step 1.3.2

Rewrite the expression.

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

Step 1.4

Evaluate the exponent.

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

Step 1.5

Rewrite $9$ as $3^{2}$ .

${(9 - {(3^{2})}^{\frac{1}{2}})}^{2}$

Step 1.6

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

${(9 - 3^{2 (\frac{1}{2})})}^{2}$

Step 1.7

Cancel the common factor of $2$ .

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Step 1.7.1

Cancel the common factor.

${(9 - 3^{2 (\frac{1}{2})})}^{2}$

Step 1.7.2

Rewrite the expression.

${(9 - 3^{1})}^{2}$

Step 1.8

Evaluate the exponent.

${(9 - 1 \cdot 3)}^{2}$

Step 1.9

Multiply $- 1$ by $3$ .

${(9 - 3)}^{2}$

Step 2

Simplify the expression.

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Step 2.1

Subtract $3$ from $9$ .

$6^{2}$

Step 2.2

Raise $6$ to the power of $2$ .

$36$