Algebra Examples

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

Step 1

Move $3^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Multiply $3^{0}$ by $3^{2}$ by adding the exponents.

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Step 2.1

Move $3^{2}$ .

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

Step 2.2

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

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

Step 2.3

Add $2$ and $0$ .

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

Step 3

Cancel the common factor of $4^{2}$ and $4^{3}$ .

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Step 3.1

Multiply by $1$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $4^{2}$ out of $3^{2} \cdot 4^{3}$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

Simplify the expression.

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Step 4.1

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

$\frac{1}{9 \cdot 4}$

Step 4.2

Multiply $9$ by $4$ .

$\frac{1}{36}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{36}$

Decimal Form:

$0.02\overline{7}$