Evaluate (4^-5)/(4^4)*4^-5

$\frac{4^{- 5}}{4^{4}} \cdot 4^{- 5}$

Step 1

Simplify the numerator.

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

$\frac{\frac{1}{4^{5}}}{4^{4}} \cdot 4^{- 5}$

Raise $4$ to the power of $5$ .

$\frac{\frac{1}{1024}}{4^{4}} \cdot 4^{- 5}$

Step 2

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

$\frac{\frac{1}{1024}}{256} \cdot 4^{- 5}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{1024} \cdot \frac{1}{256} \cdot 4^{- 5}$

Step 4

Multiply $\frac{1}{1024} \cdot \frac{1}{256}$ .

Multiply $\frac{1}{1024}$ by $\frac{1}{256}$ .

$\frac{1}{1024 \cdot 256} \cdot 4^{- 5}$

Multiply $1024$ by $256$ .

$\frac{1}{262144} \cdot 4^{- 5}$

Step 5

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

$\frac{1}{262144} \cdot \frac{1}{4^{5}}$

Step 6

Combine fractions.

Combine.

$\frac{1 \cdot 1}{262144 \cdot 4^{5}}$

Multiply $1$ by $1$ .

$\frac{1}{262144 \cdot 4^{5}}$

Step 7

Simplify the denominator.

Rewrite $262144$ as $2^{18}$ .

$\frac{1}{2^{18} \cdot 4^{5}}$

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

$\frac{1}{2^{18} \cdot {(2^{2})}^{5}}$

Multiply the exponents in ${(2^{2})}^{5}$ .

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

$\frac{1}{2^{18} \cdot 2^{2 \cdot 5}}$

Multiply $2$ by $5$ .

$\frac{1}{2^{18} \cdot 2^{10}}$

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

$\frac{1}{2^{18 + 10}}$

Add $18$ and $10$ .

$\frac{1}{2^{28}}$

Step 8

Raise $2$ to the power of $28$ .

$\frac{1}{268435456}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{268435456}$

Decimal Form:

$3.72529029 \cdot 10^{- 9}$

Evaluate (4^-5)/(4^4)*4^-5

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