Solve (3)(2^-5)^2*4^2*8^2

$$( 3 ) ( 2 ^ { - 5 } ) ^ { 2 } \times 4 ^ { 2 } \times 8 ^ { 2 }$$

Evaluate

$$3$$

Solution Steps

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

$$3\times 2^{-10}\times 4^{2}\times 8^{2}$$

Calculate 2 to the power of -10 and get \frac{1}{1024}.

$$3\times \frac{1}{1024}\times 4^{2}\times 8^{2}$$

Multiply 3 and \frac{1}{1024} to get \frac{3}{1024}.

$$\frac{3}{1024}\times 4^{2}\times 8^{2}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{3}{1024}\times 16\times 8^{2}$$

Multiply \frac{3}{1024} and 16 to get \frac{3}{64}.

$$\frac{3}{64}\times 8^{2}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{3}{64}\times 64$$

Multiply \frac{3}{64} and 64 to get 3.

$$3$$

Factor

$$3$$