Solve (7^-3)(5^2)div(5^3)(7^-4)

$$( 7 ^ { - 3 } ) ( 5 ^ { 2 } ) \div ( 5 ^ { 3 } ) ( 7 ^ { - 4 } )$$

Evaluate

$$\frac{1}{4117715}\approx 0.000000243$$

Solution Steps

Cancel out 5^{2} in both numerator and denominator.

$$\frac{7^{-3}}{5}\times 7^{-4}$$

Calculate 7 to the power of -3 and get \frac{1}{343}.

$$\frac{\frac{1}{343}}{5}\times 7^{-4}$$

Express \frac{\frac{1}{343}}{5} as a single fraction.

$$\frac{1}{343\times 5}\times 7^{-4}$$

Multiply 343 and 5 to get 1715.

$$\frac{1}{1715}\times 7^{-4}$$

Calculate 7 to the power of -4 and get \frac{1}{2401}.

$$\frac{1}{1715}\times \frac{1}{2401}$$

Multiply \frac{1}{1715} and \frac{1}{2401} to get \frac{1}{4117715}.

$$\frac{1}{4117715}$$

Factor

$$\frac{1}{5 \cdot 7 ^ {7}} = 2.428531357804025 \times 10^{-7}$$