Solve 4^3/4^5=4^3-5=1/4

$$\frac { 4 ^ { 3 } } { 4 ^ { 5 } } = 4 ^ { 3 - 5 } = \frac { 1 } { 4 }$$

Verify

Solution Steps

Rewrite 4^{5} as 4^{3}\times 4^{2}. Cancel out 4^{3} in both numerator and denominator.

$$\frac{1}{4^{2}}=4^{3-5}\text{ and }4^{3-5}=\frac{1}{4}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{1}{16}=4^{3-5}\text{ and }4^{3-5}=\frac{1}{4}$$

Subtract 5 from 3 to get -2.

$$\frac{1}{16}=4^{-2}\text{ and }4^{3-5}=\frac{1}{4}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{1}{16}=\frac{1}{16}\text{ and }4^{3-5}=\frac{1}{4}$$

Compare \frac{1}{16} and \frac{1}{16}.

$$\text{true}\text{ and }4^{3-5}=\frac{1}{4}$$

Subtract 5 from 3 to get -2.

$$\text{true}\text{ and }4^{-2}=\frac{1}{4}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\text{true}\text{ and }\frac{1}{16}=\frac{1}{4}$$

Least common multiple of 16 and 4 is 16. Convert \frac{1}{16} and \frac{1}{4} to fractions with denominator 16.

$$\text{true}\text{ and }\frac{1}{16}=\frac{4}{16}$$

Compare \frac{1}{16} and \frac{4}{16}.

$$\text{true}\text{ and }\text{false}$$

The conjunction of \text{true} and \text{false} is \text{false}.

$$\text{false}$$