Basic Math Examples

${(\frac{2}{3})}^{- 2} (\frac{9}{16})$

Step 1

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

${(\frac{3}{2})}^{2} \frac{9}{16}$

Step 2

Combine fractions.

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Step 2.1

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

$\frac{3^{2}}{2^{2}} \cdot \frac{9}{16}$

Step 2.2

Combine.

$\frac{3^{2} \cdot 9}{2^{2} \cdot 16}$

Step 3

Simplify the numerator.

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Step 3.1

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

$\frac{3^{2} \cdot 3^{2}}{2^{2} \cdot 16}$

Step 3.2

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

$\frac{3^{2 + 2}}{2^{2} \cdot 16}$

Step 3.3

Add $2$ and $2$ .

$\frac{3^{4}}{2^{2} \cdot 16}$

Step 4

Simplify the denominator.

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

Add $2$ and $4$ .

$\frac{3^{4}}{2^{6}}$

Step 5

Evaluate the exponents.

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Step 5.1

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

$\frac{81}{2^{6}}$

Step 5.2

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

$\frac{81}{64}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{81}{64}$

Decimal Form:

$1.265625$

Mixed Number Form:

$1 \frac{17}{64}$