Basic Math Examples

${(\frac{16}{9})}^{\frac{1}{2}}$

Step 1

Apply the product rule to $\frac{16}{9}$ .

$\frac{16^{\frac{1}{2}}}{9^{\frac{1}{2}}}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $16$ as $4^{2}$ .

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

Step 2.2

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

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

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Cancel the common factor.

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

Step 2.3.2

Rewrite the expression.

$\frac{4^{1}}{9^{\frac{1}{2}}}$

Step 2.4

Evaluate the exponent.

$\frac{4}{9^{\frac{1}{2}}}$

Step 3

Simplify the denominator.

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Step 3.1

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

$\frac{4}{{(3^{2})}^{\frac{1}{2}}}$

Step 3.2

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

$\frac{4}{3^{2 (\frac{1}{2})}}$

Step 3.3

Cancel the common factor of $2$ .

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Step 3.3.1

Cancel the common factor.

$\frac{4}{3^{2 (\frac{1}{2})}}$

Step 3.3.2

Rewrite the expression.

$\frac{4}{3^{1}}$

Step 3.4

Evaluate the exponent.

$\frac{4}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{3}$

Decimal Form:

$1.\overline{3}$

Mixed Number Form:

$1 \frac{1}{3}$