Solve 2^264/left(4^2right)^33

$$\frac{ { 2 }^{ 2 } 64 }{ { \left( { 4 }^{ 2 } \right) }^{ 33 } }$$

Evaluate

$$\frac{1}{21267647932558653966460912964485513216}=4.701977403 \cdot 10^{-38}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 33 to get 66.

$$\frac{2^{2}\times 64}{4^{66}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4\times 64}{4^{66}}$$

Multiply 4 and 64 to get 256.

$$\frac{256}{4^{66}}$$

Calculate 4 to the power of 66 and get 5444517870735015415413993718908291383296.

$$\frac{256}{5444517870735015415413993718908291383296}$$

Reduce the fraction \frac{256}{5444517870735015415413993718908291383296} to lowest terms by extracting and canceling out 256.

$$\frac{1}{21267647932558653966460912964485513216}$$

Factor

$$\frac{1}{2 ^ {124}} = 4.70197740328915 \times 10^{-38}$$