Question

4^x • 4^y = 1024
What is x + y?

Answer 1

x + y = 5

Explanation:

using the rule of exponents

`a^(m)` ×
`a^(n)` =
`a^(m+n)` , then

`4^(x)` ×
`4^(y)` =
`4^(x+y)` , so

`4^(x+y)` = 1024 =
`4^(5)`

since the bases on both sides are equal, both 4 then equate exponents

x + y = 5

Answer 2

x + y = 5

Explanation:

`{4}^(x) . {4}^(y) = 1024 \\ \\ {4}^(x + y) = {4}^(5) \\ \\ x + y = 5`