Basic Math Examples

${(81 \div 100)}^{- 1 \div 2}$

Step 1

Rewrite the division as a fraction.

${(\frac{81}{100})}^{- 1 \div 2}$

Step 2

Rewrite the division as a fraction.

${(\frac{81}{100})}^{\frac{- 1}{2}}$

Step 3

Move the negative in front of the fraction.

${(\frac{81}{100})}^{- \frac{1}{2}}$

Step 4

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{100}{81})}^{\frac{1}{2}}$

Step 5

Apply the product rule to $\frac{100}{81}$ .

$\frac{100^{\frac{1}{2}}}{81^{\frac{1}{2}}}$

Step 6

Simplify the numerator.

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Step 6.1

Rewrite $100$ as $10^{2}$ .

$\frac{{(10^{2})}^{\frac{1}{2}}}{81^{\frac{1}{2}}}$

Step 6.2

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

$\frac{10^{2 (\frac{1}{2})}}{81^{\frac{1}{2}}}$

Step 6.3

Cancel the common factor of $2$ .

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Step 6.3.1

Cancel the common factor.

$\frac{10^{2 (\frac{1}{2})}}{81^{\frac{1}{2}}}$

Step 6.3.2

Rewrite the expression.

$\frac{10^{1}}{81^{\frac{1}{2}}}$

Step 6.4

Evaluate the exponent.

$\frac{10}{81^{\frac{1}{2}}}$

Step 7

Simplify the denominator.

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Step 7.1

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

$\frac{10}{{(9^{2})}^{\frac{1}{2}}}$

Step 7.2

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

$\frac{10}{9^{2 (\frac{1}{2})}}$

Step 7.3

Cancel the common factor of $2$ .

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Step 7.3.1

Cancel the common factor.

$\frac{10}{9^{2 (\frac{1}{2})}}$

Step 7.3.2

Rewrite the expression.

$\frac{10}{9^{1}}$

Step 7.4

Evaluate the exponent.

$\frac{10}{9}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{10}{9}$

Decimal Form:

$1.\overline{1}$

Mixed Number Form:

$1 \frac{1}{9}$