Algebra Examples

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

Step 1

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

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

Step 2

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

$\frac{1}{8} \cdot 4^{- 9}$

Step 3

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

$\frac{1}{8} \cdot \frac{1}{4^{9}}$

Step 4

Combine fractions.

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Step 4.1

Combine.

$\frac{1 \cdot 1}{8 \cdot 4^{9}}$

Step 4.2

Multiply $1$ by $1$ .

$\frac{1}{8 \cdot 4^{9}}$

Step 5

Simplify the denominator.

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Step 5.1

Rewrite $8$ as $2^{3}$ .

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

Step 5.2

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

$\frac{1}{2^{3} \cdot {(2^{2})}^{9}}$

Step 5.3

Multiply the exponents in ${(2^{2})}^{9}$ .

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Step 5.3.1

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

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

Step 5.3.2

Multiply $2$ by $9$ .

$\frac{1}{2^{3} \cdot 2^{18}}$

Step 5.4

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

$\frac{1}{2^{3 + 18}}$

Step 5.5

Add $3$ and $18$ .

$\frac{1}{2^{21}}$

Step 6

Raise $2$ to the power of $21$ .

$\frac{1}{2097152}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2097152}$

Decimal Form:

$4.76837158 \cdot 10^{- 7}$