Solve [(11^3/11^2)^-2]^3

$$[ ( \frac { 11 ^ { 3 } } { 11 ^ { 2 } } ) ^ { - 2 } ] ^ { 3 }$$

Evaluate

$$\frac{1}{1771561}\approx 0.000000564$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 3 to get 1.

$$\left(\left(11^{1}\right)^{-2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 1 and -2 to get -2.

$$\left(11^{-2}\right)^{3}$$

Calculate 11 to the power of -2 and get \frac{1}{121}.

$$\left(\frac{1}{121}\right)^{3}$$

Calculate \frac{1}{121} to the power of 3 and get \frac{1}{1771561}.

$$\frac{1}{1771561}$$

Factor

$$\frac{1}{11 ^ {6}} = 5.644739300537775 \times 10^{-7}$$