Simplify (4^-8)/(4^-7)*4^0

$\frac{4^{- 8}}{4^{- 7}} \cdot 4^{0}$

Step 1

Simplify the numerator.

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

$\frac{\frac{1}{4^{8}}}{4^{- 7}} \cdot 4^{0}$

Raise $4$ to the power of $8$ .

$\frac{\frac{1}{65536}}{4^{- 7}} \cdot 4^{0}$

Step 2

Simplify the denominator.

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

$\frac{\frac{1}{65536}}{\frac{1}{4^{7}}} \cdot 4^{0}$

Raise $4$ to the power of $7$ .

$\frac{\frac{1}{65536}}{\frac{1}{16384}} \cdot 4^{0}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{65536} \cdot 16384 \cdot 4^{0}$

Step 4

Cancel the common factor of $16384$ .

Factor $16384$ out of $65536$ .

$\frac{1}{16384 (4)} \cdot 16384 \cdot 4^{0}$

Cancel the common factor.

$\frac{1}{16384 \cdot 4} \cdot 16384 \cdot 4^{0}$

Rewrite the expression.

$\frac{1}{4} \cdot 4^{0}$

Step 5

Simplify the expression.

Anything raised to $0$ is $1$ .

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

Multiply $\frac{1}{4}$ by $1$ .

$\frac{1}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4}$

Decimal Form:

$0.25$