Question

Which of the following is equivalent to

Answer 1

`x^(4)`

Explanation:

`(x^(5)y^(2)  )/(xy^(2) )`

=
`x^(4)`

Answer 2

Question 1:

For this case we have the following expression:

`\frac {x ^ 5y ^ 2} {xy ^ 2}`

We eliminate similar terms in the numerator and denominator:

`\frac {x ^ 5} {x}`

By definition of division of powers of the same base we have to place the same base and subtract the exponents:

`\frac {x ^ 5} {x} = x ^ {5-1} = x ^ 4`

ANswer:

Option D

Question 2:

For this case we must indicate which expression is not equal to 125.

We tested option A:

`5 (\frac {5 ^ 3} {\frac {2} {5}}) ^ 2 =`

Simplifying we have:

`5 (\frac {5 ^ 3 * 5} {2}) ^ 2 =\\5 (\frac {5 ^ 8} {4}) =\\\frac {5 ^ 9} {4}`

The expression is not equal to 125.

Answer:

option A