Final answer:
To express a number as a power of 2, we need to find the exponent that, when applied to 2, gives us the number. We can rewrite 16^8 as 2^32. In the expression 4^(3p-1), we can simplify it to 2^(6p-2). Similarly, we can express 32^4 ÷ 5 as 2^20 ÷ 5.
Step-by-step explanation:
In order to express a number as a power of 2, we need to find the exponent that, when applied to 2, gives us the given number. Let's solve each part of the question:
A.) 16^8:
We know that 16 is equal to 2^4. So, we can rewrite 16^8 as (2^4)^8. Applying the exponent rule that says (a^b)^c = a^(b*c), we get 2^(4*8) = 2^32.
B.) 4^(3p-1):
There's no direct way to express this expression as a power of 2 because we have a variable (p) in the exponent. However, we can still simplify the expression. Expanding 4^(3p-1) gives us (2^2)^(3p-1), which simplifies to 2^(2*(3p-1)) = 2^(6p-2).
C.) 32^4 ÷ 5:
32 is equal to 2^5, so 32^4 is equal to (2^5)^4. Using the exponent rule mentioned earlier, we get 2^(5*4) = 2^20. Dividing this by 5 gives us 2^20 ÷ 5.