Solve 3^-2+5^-3/3^-2-5^-2

$$\frac { 3 ^ { - 2 } + 5 ^ { - 3 } } { 3 ^ { - 2 } - 5 ^ { - 2 } }$$

Evaluate

$$\frac{67}{40}=1.675$$

Solution Steps

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{9}+5^{-3}}{3^{-2}-5^{-2}}$$

Calculate 5 to the power of -3 and get \frac{1}{125}.

$$\frac{\frac{1}{9}+\frac{1}{125}}{3^{-2}-5^{-2}}$$

Add \frac{1}{9} and \frac{1}{125} to get \frac{134}{1125}.

$$\frac{\frac{134}{1125}}{3^{-2}-5^{-2}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{134}{1125}}{\frac{1}{9}-5^{-2}}$$

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{\frac{134}{1125}}{\frac{1}{9}-\frac{1}{25}}$$

Subtract \frac{1}{25} from \frac{1}{9} to get \frac{16}{225}.

$$\frac{\frac{134}{1125}}{\frac{16}{225}}$$

Divide \frac{134}{1125} by \frac{16}{225} by multiplying \frac{134}{1125} by the reciprocal of \frac{16}{225}.

$$\frac{134}{1125}\times \frac{225}{16}$$

Multiply \frac{134}{1125} and \frac{225}{16} to get \frac{67}{40}.

$$\frac{67}{40}$$

Factor

$$\frac{67}{2 ^ {3} \cdot 5} = 1\frac{27}{40} = 1.675$$