Solve (2^-10/4^2)^7=?

$$( \frac { 2 ^ { - 10 } } { 4 ^ { 2 } } ) ^ { 7 } = ?$$

Evaluate

$$\frac{1}{316912650057057350374175801344}=3.155443621 \cdot 10^{-30}$$

Solution Steps

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

$$\left(\frac{\frac{1}{1024}}{4^{2}}\right)^{7}$$

Calculate 4 to the power of 2 and get 16.

$$\left(\frac{\frac{1}{1024}}{16}\right)^{7}$$

Express \frac{\frac{1}{1024}}{16} as a single fraction.

$$\left(\frac{1}{1024\times 16}\right)^{7}$$

Multiply 1024 and 16 to get 16384.

$$\left(\frac{1}{16384}\right)^{7}$$

Calculate \frac{1}{16384} to the power of 7 and get \frac{1}{316912650057057350374175801344}.

$$\frac{1}{316912650057057350374175801344}$$

Factor

$$\frac{1}{2 ^ {98}} = 3.155443620884047 \times 10^{-30}$$