Question

"Simplify to a single power of 2:
(2^4)^5

Answer 1

The simplification of (2^4)^5 to a single power of 2 is 2^(4×5), which equals 2^20.

Step-by-step explanation:

To simplify (2^4)^5 to a single power of 2, we apply the rule of exponents that states when a power is raised to another power, you multiply the exponents. In this case, we have the base number 2 raised to the power of 4, and this result is again raised to the power of 5.

Using the rule:

(2^4)^5 = 2^(4×5) = 2^20

This simplification is possible because of how exponentiation works; when we raise a number to a power, we are simply multiplying that number by itself a certain number of times, and when we raise this expression to another power, we are multiplying the number of times again. So, effectively, we are multiplying the exponents (4 and 5 in this case) to get the overall power (20).