Solve 8^-216/16^-264^2

$$\frac{ { 8 }^{ -2 } 16 }{ { 16 }^{ -2 } } { 64 }^{ 2 }$$

Evaluate

$$262144$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$8^{-2}\times 16^{3}\times 64^{2}$$

Calculate 16 to the power of 3 and get 4096.

$$8^{-2}\times 4096\times 64^{2}$$

Calculate 64 to the power of 2 and get 4096.

$$8^{-2}\times 4096\times 4096$$

Multiply 4096 and 4096 to get 16777216.

$$8^{-2}\times 16777216$$

Calculate 8 to the power of -2 and get \frac{1}{64}.

$$\frac{1}{64}\times 16777216$$

Multiply \frac{1}{64} and 16777216 to get 262144.

$$262144$$

Factor

$$2^{18}$$