Solve 1/36(1/36)^(frac{-1{2})^-1}+((1/64)^3)^-1

$$\frac { 1 } { 36 } ( \frac { 1 } { 36 } ) ^ { ( \frac { - 1 } { 2 } ) ^ { - 1 } } + ( ( \frac { 1 } { 64 } ) ^ { 3 } ) ^ { - 1 }$$

Evaluate

$$262180$$

Solution Steps

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

$$\frac{1}{36}\times \left(\frac{1}{36}\right)^{\left(\frac{-1}{2}\right)^{-1}}+\left(\frac{1}{64}\right)^{-3}$$

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$\frac{1}{36}\times \left(\frac{1}{36}\right)^{\left(-\frac{1}{2}\right)^{-1}}+\left(\frac{1}{64}\right)^{-3}$$

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

$$\frac{1}{36}\times \left(\frac{1}{36}\right)^{-2}+\left(\frac{1}{64}\right)^{-3}$$

Calculate \frac{1}{36} to the power of -2 and get 1296.

$$\frac{1}{36}\times 1296+\left(\frac{1}{64}\right)^{-3}$$

Multiply \frac{1}{36} and 1296 to get 36.

$$36+\left(\frac{1}{64}\right)^{-3}$$

Calculate \frac{1}{64} to the power of -3 and get 262144.

$$36+262144$$

Add 36 and 262144 to get 262180.

$$262180$$

Factor

$$2^{2}\times 5\times 13109$$