Solve 4^-2-9^-2/(6^-2)^2

$$\frac { 4 ^ { - 2 } - 9 ^ { - 2 } } { ( 6 ^ { - 2 } ) ^ { 2 } }$$

Evaluate

$$65$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -2 and 2 to get -4.

$$\frac{4^{-2}-9^{-2}}{6^{-4}}$$

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

$$\frac{\frac{1}{16}-9^{-2}}{6^{-4}}$$

Calculate 9 to the power of -2 and get \frac{1}{81}.

$$\frac{\frac{1}{16}-\frac{1}{81}}{6^{-4}}$$

Subtract \frac{1}{81} from \frac{1}{16} to get \frac{65}{1296}.

$$\frac{\frac{65}{1296}}{6^{-4}}$$

Calculate 6 to the power of -4 and get \frac{1}{1296}.

$$\frac{\frac{65}{1296}}{\frac{1}{1296}}$$

Divide \frac{65}{1296} by \frac{1}{1296} by multiplying \frac{65}{1296} by the reciprocal of \frac{1}{1296}.

$$\frac{65}{1296}\times 1296$$

Multiply \frac{65}{1296} and 1296 to get 65.

$$65$$

Factor

$$5\times 13$$