Solve (7^-3)^-1/(7^3)^3

$$\frac { ( 7 ^ { - 3 } ) ^ { - 1 } } { ( 7 ^ { 3 } ) ^ { 3 } }$$

Evaluate

$$\frac{1}{117649}\approx 0.0000085$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -3 and -1 to get 3.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{7^{3}}{7^{9}}$$

Rewrite 7^{9} as 7^{3}\times 7^{6}. Cancel out 7^{3} in both numerator and denominator.

$$\frac{1}{7^{6}}$$

Calculate 7 to the power of 6 and get 117649.

$$\frac{1}{117649}$$

Factor

$$\frac{1}{7 ^ {6}} = 8.499859752314087 \times 10^{-6}$$