Solve 5^-8>1/32,000>1/3^7

$$5 ^ { - 8 } > \frac { 1 } { 32,000 } > \frac { 1 } { 3 ^ { 7 } }$$

Verify

Solution Steps

Calculate 5 to the power of -8 and get \frac{1}{390625}.

$$\frac{1}{390625}>\frac{1}{32000}\text{ and }\frac{1}{32000}>\frac{1}{3^{7}}$$

Least common multiple of 390625 and 32000 is 100000000. Convert \frac{1}{390625} and \frac{1}{32000} to fractions with denominator 100000000.

$$\frac{256}{100000000}>\frac{3125}{100000000}\text{ and }\frac{1}{32000}>\frac{1}{3^{7}}$$

Compare \frac{256}{100000000} and \frac{3125}{100000000}.

$$\text{false}\text{ and }\frac{1}{32000}>\frac{1}{3^{7}}$$

Calculate 3 to the power of 7 and get 2187.

$$\text{false}\text{ and }\frac{1}{32000}>\frac{1}{2187}$$

Least common multiple of 32000 and 2187 is 69984000. Convert \frac{1}{32000} and \frac{1}{2187} to fractions with denominator 69984000.

$$\text{false}\text{ and }\frac{2187}{69984000}>\frac{32000}{69984000}$$

Compare \frac{2187}{69984000} and \frac{32000}{69984000}.

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

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

$$\text{false}$$