Algebra Examples

$(2^{- 3} \cdot 3^{- 5}) (2^{4} \cdot 3^{3})$

Step 1

Multiply $2^{- 3}$ by $2^{4}$ by adding the exponents.

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Step 1.1

Move $2^{4}$ .

$2^{4} \cdot 2^{- 3} \cdot 3^{- 5} \cdot 3^{3}$

Step 1.2

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

$2^{4 - 3} \cdot 3^{- 5} \cdot 3^{3}$

Step 1.3

Subtract $3$ from $4$ .

$2^{1} \cdot 3^{- 5} \cdot 3^{3}$

Step 2

Simplify $2^{1} \cdot 3^{- 5} \cdot 3^{3}$ .

$2 \cdot 3^{- 5} \cdot 3^{3}$

Step 3

Multiply $3^{- 5}$ by $3^{3}$ by adding the exponents.

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Step 3.1

Move $3^{3}$ .

$2 \cdot (3^{3} \cdot 3^{- 5})$

Step 3.2

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

$2 \cdot 3^{3 - 5}$

Step 3.3

Subtract $5$ from $3$ .

$2 \cdot 3^{- 2}$

Step 4

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

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

Step 5

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

$2 \cdot \frac{1}{9}$

Step 6

Combine $2$ and $\frac{1}{9}$ .

$\frac{2}{9}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{9}$

Decimal Form:

$0.\overline{2}$