Solve 4^20*4^2:(4^5)^9

$$4 ^ { 20 } \cdot 4 ^ { 2 } : ( 4 ^ { 5 } ) ^ { 9 }$$

Evaluate

$$\frac{1}{70368744177664}=1.421085472 \cdot 10^{-14}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 20 and 2 to get 22.

$$\frac{4^{22}}{\left(4^{5}\right)^{9}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 9 to get 45.

$$\frac{4^{22}}{4^{45}}$$

Rewrite 4^{45} as 4^{22}\times 4^{23}. Cancel out 4^{22} in both numerator and denominator.

$$\frac{1}{4^{23}}$$

Calculate 4 to the power of 23 and get 70368744177664.

$$\frac{1}{70368744177664}$$

Factor

$$\frac{1}{2 ^ {46}} = 1.4210854715202004 \times 10^{-14}$$