Solve 1/64(1/64)^(frac{-1{2})^-1}+((1/8)^3)^-1

$$\frac { 1 } { 64 } ( \frac { 1 } { 64 } ) ^ { ( \frac { - 1 } { 2 } ) ^ { - 1 } } + ( ( \frac { 1 } { 8 } ) ^ { 3 } ) ^ { - 1 }$$

Evaluate

$$576$$

Solution Steps

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

$$\frac{1}{64}\times \left(\frac{1}{64}\right)^{\left(\frac{-1}{2}\right)^{-1}}+\left(\frac{1}{8}\right)^{-3}$$

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

$$\frac{1}{64}\times \left(\frac{1}{64}\right)^{\left(-\frac{1}{2}\right)^{-1}}+\left(\frac{1}{8}\right)^{-3}$$

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

$$\frac{1}{64}\times \left(\frac{1}{64}\right)^{-2}+\left(\frac{1}{8}\right)^{-3}$$

Calculate \frac{1}{64} to the power of -2 and get 4096.

$$\frac{1}{64}\times 4096+\left(\frac{1}{8}\right)^{-3}$$

Multiply \frac{1}{64} and 4096 to get 64.

$$64+\left(\frac{1}{8}\right)^{-3}$$

Calculate \frac{1}{8} to the power of -3 and get 512.

$$64+512$$

Add 64 and 512 to get 576.

$$576$$

Factor

$$2^{6}\times 3^{2}$$