Solve (7^-3)^-2/(7^3)^8

$$\frac { ( 7 ^ { - 3 } ) ^ { - 2 } } { ( 7 ^ { 3 } ) ^ { 8 } }$$

Evaluate

$$\frac{1}{1628413597910449}\approx 6.140946018 \cdot 10^{-16}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -3 and -2 to get 6.

$$\frac{7^{6}}{\left(7^{3}\right)^{8}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 8 to get 24.

$$\frac{7^{6}}{7^{24}}$$

Rewrite 7^{24} as 7^{6}\times 7^{18}. Cancel out 7^{6} in both numerator and denominator.

$$\frac{1}{7^{18}}$$

Calculate 7 to the power of 18 and get 1628413597910449.

$$\frac{1}{1628413597910449}$$

Factor

$$\frac{1}{7 ^ {18}} = 6.1409460181564555 \times 10^{-16}$$