Basic Math Examples

${(\frac{2}{3})}^{2} (4^{0}) (3^{- 2})$

Step 1

Apply the product rule to $\frac{2}{3}$ .

$\frac{2^{2}}{3^{2}} \cdot 4^{0} \cdot 3^{- 2}$

Step 2

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

$\frac{4}{3^{2}} \cdot 4^{0} \cdot 3^{- 2}$

Step 3

Raise $3$ to the power of $2$ .

$\frac{4}{9} \cdot 4^{0} \cdot 3^{- 2}$

Step 4

Anything raised to $0$ is $1$ .

$\frac{4}{9} \cdot 1 \cdot 3^{- 2}$

Step 5

Multiply $\frac{4}{9}$ by $1$ .

$\frac{4}{9} \cdot 3^{- 2}$

Step 6

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{4}{9} \cdot \frac{1}{3^{2}}$

Step 7

Combine fractions.

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Step 7.1

Combine.

$\frac{4 \cdot 1}{9 \cdot 3^{2}}$

Step 7.2

Multiply $4$ by $1$ .

$\frac{4}{9 \cdot 3^{2}}$

Step 8

Simplify the denominator.

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Step 8.1

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

$\frac{4}{3^{2} \cdot 3^{2}}$

Step 8.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4}{3^{2 + 2}}$

Step 8.3

Add $2$ and $2$ .

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

Step 9

Raise $3$ to the power of $4$ .

$\frac{4}{81}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{81}$

Decimal Form:

$0.04938271 \dots$