Solve 4^2*4^-4/4^7*4^-5

$$\frac { 4 ^ { 2 } \cdot 4 ^ { - 4 } } { 4 ^ { 7 } \cdot 4 ^ { - 5 } }$$

Evaluate

$$\frac{1}{256}=0.00390625$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and -4 to get -2.

$$\frac{4^{-2}}{4^{7}\times 4^{-5}}$$

To multiply powers of the same base, add their exponents. Add 7 and -5 to get 2.

$$\frac{4^{-2}}{4^{2}}$$

Rewrite 4^{2} as 4^{-2}\times 4^{4}. Cancel out 4^{-2} in both numerator and denominator.

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

Calculate 4 to the power of 4 and get 256.

$$\frac{1}{256}$$

Factor

$$\frac{1}{2 ^ {8}} = 0.00390625$$