Solve [1/6-1/36]div[(5/6)^2(5^-1)*5^2]

$$[ \frac { 1 } { 6 } - \frac { 1 } { 36 } ] \div [ ( \frac { 5 } { 6 } ) ^ { 2 } ( 5 ^ { - 1 } ) \cdot 5 ^ { 2 } ]$$

Evaluate

$$\frac{1}{25}=0.04$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -1 and 2 to get 1.

$$\frac{\frac{1}{6}-\frac{1}{36}}{\left(\frac{5}{6}\right)^{2}\times 5^{1}}$$

Subtract \frac{1}{36} from \frac{1}{6} to get \frac{5}{36}.

$$\frac{\frac{5}{36}}{\left(\frac{5}{6}\right)^{2}\times 5^{1}}$$

Calculate \frac{5}{6} to the power of 2 and get \frac{25}{36}.

$$\frac{\frac{5}{36}}{\frac{25}{36}\times 5^{1}}$$

Calculate 5 to the power of 1 and get 5.

$$\frac{\frac{5}{36}}{\frac{25}{36}\times 5}$$

Multiply \frac{25}{36} and 5 to get \frac{125}{36}.

$$\frac{\frac{5}{36}}{\frac{125}{36}}$$

Divide \frac{5}{36} by \frac{125}{36} by multiplying \frac{5}{36} by the reciprocal of \frac{125}{36}.

$$\frac{5}{36}\times \frac{36}{125}$$

Multiply \frac{5}{36} and \frac{36}{125} to get \frac{1}{25}.

$$\frac{1}{25}$$

Factor

$$\frac{1}{5 ^ {2}} = 0.04$$