powers can be used to express some numbers in several ways for example 64 can be expressed as 43 or 26 or 82 write each number in two ways as powers a) 16 b) 81 c) 256 d) 1024
16 = 2^4 = 4^2
your turn
write powers this way:
4^3 , 2^6, etc
b) 81 = 9^2 or 3^4
try the others, let me know what you get
hint sqrt (1024) = 32
To express a number in terms of powers, we need to find the base and the exponent that will give us that number.
a) To express 16 in two ways as powers:
16 can be written as 2^4 since 2 * 2 * 2 * 2 = 16.
Alternatively, 16 can also be written as 4^2 since 4 * 4 = 16.
b) To express 81 in two ways as powers:
81 can be written as 3^4 since 3 * 3 * 3 * 3 = 81.
Similarly, 81 can also be written as 9^2 since 9 * 9 = 81.
c) To express 256 in two ways as powers:
256 can be written as 2^8 since 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 256.
Alternatively, 256 can also be written as 16^2 since 16 * 16 = 256.
d) To express 1024 in two ways as powers:
1024 can be written as 2^10 since 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 1024.
Similarly, 1024 can also be written as 32^2 since 32 * 32 = 1024.
By using the concept of exponentiation, we can find different ways to express numbers as powers.