Question

NEED HELP WITH THESE QUESTIONS

Answer 1

17. The correct answer option is A.

18. The correct answer option is D.

19. The correct answer option is D.

Explanation:

17.
`(m^2n^3)/(p^3) * (mp)/(n^2)`

Changing division to multiplication by taking reciprocal of the latter fraction to get:

`(m^2n^3)/(p^3) * (n^2)/(mp)`

`(mn^5)/(p^4)`

The correct answer option is A.
`(mn^5)/(p^4)`.

18.
`(3xyz^2)/(6y^4) * (2y)/(xz^4)`

`(1)/(y^2z^2)`

The correct answer option is D.
`(1)/(y^2z^2)`.

19.
`(r^2+7r+10)/(3) * (3r-30)/(r^2-5r-50)`

Factorizing the terms to get:

`((r+2)(r+5))/(3) * (3(r-10))/((r+5)(r-10))`

Cancelling the like terms to get:

`r+2`

The correct answer option is D.
`r+2`.

Answer 2

For this case we must solve the following questions:

Question 1:

We should simplify the following expression:

`\frac {\frac {m ^ 2 * n ^ 3} {p ^ 3}} {\frac {mp} {n ^ 2}} =`

Applying double C we have:

`\frac {m ^ 2 * n ^ 3 * n ^ 2} {mp * p ^ 3} =`

By definition of multiplication of powers of the same base we have to place the same base and add the exponents:
`\frac {m ^ 2 * n ^ 5} {m * p ^ 4} =`

Canceling common terms:

`\frac {mn ^ 5} {p ^ 4}`

Answer:

Option A

Question 2:

We should simplify the following expression:

`\frac {3xyz ^ 2} {6y ^ 4} * \frac {2y} {xz ^ 4}`

So, we have:

`\frac {3xyz ^ 2 * 2y} {6y ^ 4 * xz ^ 4} =\\\frac {6xy ^ 2z ^ 2} {6y ^ 4xz ^ 4} =`

Simplifying common terms:

`\frac {1} {y ^ 2z ^ 2}`

Answer:

Option D

Question 3:

We factor the following expressions to rewrite the experience:

`r ^ 2 + 7r + 10`: We look for two numbers that multiplied give 10 and added 7:

`(r + 5) (r + 2)`

`r ^ 2-5r-50:` We look for two numbers that multiplied give -50 and added -5:

`(r-10) (r + 5)`

`3r-30 = 3 (r-10)`

Rewriting the given expression we have:

`\frac {(r + 5) (r + 2) * 3 (r-10)} {3 (r-10) (r + 5)} =`

We simplify common terms in the numerator and denominator we have:

`(r + 2)`

Answer:

Option D