For this case we must solve the following questions:
Question 1:
We should simplify the following expression:
[tex]\frac {\frac {m ^ 2 * n ^ 3} {p ^ 3}} {\frac {mp} {n ^ 2}} =[/tex]
Applying double C we have:
[tex]\frac {m ^ 2 * n ^ 3 * n ^ 2} {mp * p ^ 3} =[/tex]
By definition of multiplication of powers of the same base we have to place the same base and add the exponents:[tex]\frac {m ^ 2 * n ^ 5} {m * p ^ 4} =[/tex]
Canceling common terms:
[tex]\frac {mn ^ 5} {p ^ 4}[/tex]
Answer:
Option A
Question 2:
We should simplify the following expression:
[tex]\frac {3xyz ^ 2} {6y ^ 4} * \frac {2y} {xz ^ 4}[/tex]
So, we have:
[tex]\frac {3xyz ^ 2 * 2y} {6y ^ 4 * xz ^ 4} =\\\frac {6xy ^ 2z ^ 2} {6y ^ 4xz ^ 4} =[/tex]
Simplifying common terms:
[tex]\frac {1} {y ^ 2z ^ 2}[/tex]
Answer:
Option D
Question 3:
We factor the following expressions to rewrite the experience:
[tex]r ^ 2 + 7r + 10[/tex]: We look for two numbers that multiplied give 10 and added 7:
[tex](r + 5) (r + 2)[/tex]
[tex]r ^ 2-5r-50:[/tex] We look for two numbers that multiplied give -50 and added -5:
[tex](r-10) (r + 5)[/tex]
[tex]3r-30 = 3 (r-10)[/tex]
Rewriting the given expression we have:
[tex]\frac {(r + 5) (r + 2) * 3 (r-10)} {3 (r-10) (r + 5)} =[/tex]
We simplify common terms in the numerator and denominator we have:
[tex](r + 2)[/tex]
Answer:
Option D
