Solve (4^{-1})^{4}*2^{5}*(1/16)^{3}*(8^-2)^5*(64^2)^3

$$( 4 ^ { - 1 } ) ^ { 4 } \times 2 ^ { 5 } \times ( \frac { 1 } { 16 } ) ^ { 3 } \times ( 8 ^ { - 2 } ) ^ { 5 } \times ( 64 ^ { 2 } ) ^ { 3 }$$

Evaluate

$$\frac{1}{512}=0.001953125$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -1 and 4 to get -4.

$$4^{-4}\times 2^{5}\times \left(\frac{1}{16}\right)^{3}\times \left(8^{-2}\right)^{5}\times \left(64^{2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply -2 and 5 to get -10.

$$4^{-4}\times 2^{5}\times \left(\frac{1}{16}\right)^{3}\times 8^{-10}\times \left(64^{2}\right)^{3}$$

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

$$4^{-4}\times 2^{5}\times \left(\frac{1}{16}\right)^{3}\times 8^{-10}\times 64^{6}$$

Calculate 4 to the power of -4 and get \frac{1}{256}.

$$\frac{1}{256}\times 2^{5}\times \left(\frac{1}{16}\right)^{3}\times 8^{-10}\times 64^{6}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{1}{256}\times 32\times \left(\frac{1}{16}\right)^{3}\times 8^{-10}\times 64^{6}$$

Multiply \frac{1}{256} and 32 to get \frac{1}{8}.

$$\frac{1}{8}\times \left(\frac{1}{16}\right)^{3}\times 8^{-10}\times 64^{6}$$

Calculate \frac{1}{16} to the power of 3 and get \frac{1}{4096}.

$$\frac{1}{8}\times \frac{1}{4096}\times 8^{-10}\times 64^{6}$$

Multiply \frac{1}{8} and \frac{1}{4096} to get \frac{1}{32768}.

$$\frac{1}{32768}\times 8^{-10}\times 64^{6}$$

Calculate 8 to the power of -10 and get \frac{1}{1073741824}.

$$\frac{1}{32768}\times \frac{1}{1073741824}\times 64^{6}$$

Multiply \frac{1}{32768} and \frac{1}{1073741824} to get \frac{1}{35184372088832}.

$$\frac{1}{35184372088832}\times 64^{6}$$

Calculate 64 to the power of 6 and get 68719476736.

$$\frac{1}{35184372088832}\times 68719476736$$

Multiply \frac{1}{35184372088832} and 68719476736 to get \frac{1}{512}.

$$\frac{1}{512}$$

Factor

$$\frac{1}{2 ^ {9}} = 0.001953125$$