Question

Please solve this question with explanation

Answer 1

(d) 1

Explanation:

Note this indices rule:
`(x^(m) )(x^(n) )=x^(m+n)`

What this tells us is that when you are multiply terms with the same base, the base will remain the same and the index will be the sum of the indices.

Here we are multiplying
`a^(x-y)`,
`a^(y-z)`, and
`a^(z-x)`. Each of these have the same base (
`a`), so our answer will be
`a` to the power of the sum of those three terms' indices:

`a^(x-y)` x
`a^(y-z)` x
`a^(z-x)` =
`a^(x-y+y-z+z-x)` =
`a^(0)`= 1

Answer 2

(d) 1

Explanation:

To evaluate the expression a^((x-y))*a^((y-z))*a^((z-x)), we can simplify it using the properties of exponents.

Using the rule of multiplying exponential expressions with the same base, we can combine the exponents:

a^((x-y))*a^((y-z))*a^((z-x)) = a^((x-y+y-z+z-x))

Simplifying the exponents further:

= a^((x+z-x-y+y-z))

Notice that the terms x and z cancel out, and the terms y and -y also cancel out:

= a^((0))

Any number raised to the power of 0 equals 1:

= 1

Therefore, the value of the expression a^((x-y))*a^((y-z))*a^((z-x)) is 1.