Basic Math Examples

$(32^{\frac{1}{2}} - 2^{\frac{1}{2}}) \cdot 81^{\frac{1}{2}}$

Step 1

Simplify the expression.

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Step 1.1

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

$(32^{\frac{1}{2}} - 2^{\frac{1}{2}}) \cdot {(9^{2})}^{\frac{1}{2}}$

Step 1.2

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

$(32^{\frac{1}{2}} - 2^{\frac{1}{2}}) \cdot 9^{2 (\frac{1}{2})}$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Cancel the common factor.

$(32^{\frac{1}{2}} - 2^{\frac{1}{2}}) \cdot 9^{2 (\frac{1}{2})}$

Step 2.2

Rewrite the expression.

$(32^{\frac{1}{2}} - 2^{\frac{1}{2}}) \cdot 9^{1}$

Step 3

Evaluate the exponent.

$(32^{\frac{1}{2}} - 2^{\frac{1}{2}}) \cdot 9$

Step 4

Apply the distributive property.

$32^{\frac{1}{2}} \cdot 9 - 2^{\frac{1}{2}} \cdot 9$

Step 5

Simplify the expression.

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Step 5.1

Move $9$ to the left of $32^{\frac{1}{2}}$ .

$9 \cdot 32^{\frac{1}{2}} - 2^{\frac{1}{2}} \cdot 9$

Step 5.2

Multiply $9$ by $- 1$ .

$9 \cdot 32^{\frac{1}{2}} - 9 \cdot 2^{\frac{1}{2}}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$9 \cdot 32^{\frac{1}{2}} - 9 \cdot 2^{\frac{1}{2}}$

Decimal Form:

$38.18376618 \dots$