Question

Which expression is equivalent to
`4^7*4^(-5)`? A.
`4^(12)` B.
`4^2` C.
`4^(-2)` D.
`4^(-35)`

Answer 1

`{4}^(2)`

Step by step explanation

`{4}^(7) * {4}^( - 5)`

Use product law of indices

i.e

`{x}^(m) * {x}^(n) = {x}^(m + n)`

( powers are added in multiplication of same base)

`= {4}^(7 + ( - 5))`

`= {4}^(7 - 5)`

`= {4}^(2)`

Hope this helps...

Best regards!

Answer 2

B.
`4^2`

Explanation:

`4^7 * 4^(-5)`

Apply rule (if bases are same) :
`a^b * a^c = a^(b + c)`

`4^(7 + -5)`

Add exponents.

`=4^2`