Question

There are (4^2)^3 ⋅ 4^0 horses on a stud farm. What is the total number of horses on the farm?

A. 0
B. 4^6
C. 4^7
D. 4^24

Answer 1

The answer is B
`4^(6)`.

Explanation:

The number of horses is given by the expression;

`(4^(2) )^(3) *4^(0)`

First we can simplify the value to the left of the multiplication,

`(4^(2) )^(3)`

This is a indices multiplication so we can rewrite this as,

`4^(6)`

Now we can look at the value that is to the right of the multiplication.

`4^(0)`

If you take any number that is not 0 and it's index is 0 the value of that number will be one.

Therefore,
`4^(0)` = 1

Now we can write the full expression as;

`(4^(2) )^(3) *1`

=
`(4^(2) )^(3)`

=
`4^(6)`

Therefore the answer is B
`4^(6)`.