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If \(\frac{(a^2 b^{-3}c)^{\frac{3}{4}}}{a^{-1}b^{4}c^{5}}=a^{p} b^{q} c^{r}\) What is the value of p+2q?

If \(\frac{(a^2 b^{-3}c)^{\frac{3}{4}}}{a^{-1}b^{4}c^{5}}=a^{p} b^{q} c^{r}\) What is the value of p+2q?
  • A. (5/2)
  • B. -(5/4)
  • C. -(25/4)
  • D. -10
Correct Answer: Option D
Explanation
Hint: apply basic mathematics rules beginning from BODMAS to algebra, and follow solution carefully to arrive at p =(5/2), q = -(25/4) and r = -(9/2).

Then p+2q will give you \(\frac{5}{2}+2\left(\frac{-25}{4}\right)= -10\)

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Contributions (61)

Waldon95
6 years ago
Soln

[a^2(3/4)b^-3(3/4)c^(3/4)]divided by (a^-1b^4c^5)

===>(a^3/2b^-9/4c^3/4)divided by (a^-1b^4c^5).

Note a^p =3/2-(-1)==>p=5/2

q=-9/4-(4)===>q=-25/4

r=3/4-(5)===>r=-17/4

now p+2q

5/2+2(-25/4)

:- p+2q=-10.

Make use of indice...
sunday felicia
3 years ago
I SWEAR HEE NO EASY AT ALL.IS DIS D KIND OF QUESTION WE ARE GOIN TO FACE INSIDE HALL. BEFORE I FINISHE SOLVING DIS QUESTION INSIDE EXAM HALL,DERE WOULD BE ANYTIME LEFT.MAY GOD HELP US NI O
Waldon95
6 years ago
Soln


[a^2(3/4)b^-3(3/4)c^(3/4)]divided by (a^-1b^4c^5)


===>(a^3/2b^-9/4c^3/4)divided by (a^-1b^4c^5).


Note a^p =3/2-(-1)==>p=5/2


q=-9/4-(4)===>q=-25/4


r=3/4-(5)===>r=-17/4


now p+2q


5/2+2(-25/4)


:- p+2q=-10.


Make use of indice...
Felix Powell
5 years ago
Soln

{(a^2b^-3c)^3\4 /a^-1b^4c^5} =a^pb^qc^r

from the power law of indices.

(a^2b^-3c)^3\4 =a^2*3\4.b^-3*3\4.c^1*3\4

=a^3\2.b^-9\4.c^3\4

from the divisional law of indices

(a^3\a.b^-9\4.c^3\4)/a^-1.b^4.c^5 =

a^3\2+1.b^-9\4-4.c^3\4-5

=a^5\2.b-25\4.c^-17\4

Now by comparing the powers in a^p.b^q.c^r

p=5\2,b=-25\4,c=-17\4

substituting the values of p and q in the equation p+2q,we will have

5\2 + 2(-25\4) = 5\2- 25\2

=(5-25)\2 = -20\2 = -10 Ans.
maxi957
6 years ago
This question is really great.what you need to first is to open the bracket then use indices to remove the division sign to subtraction sign then after which you compare to get p,q and r.then u can substitute it into p+2q.that's it.you just need to tink hard.
nadispeters
5 years ago
OMG am loving this site so much
Omotayo isaac
6 years ago
Is this what we want to solve in UTME......yea!I don suffer :(
prof kc
3 years ago
is this really jamb pst questions?
ahmedhalidu
5 years ago
Dont be confused,just apply the law of indices,you will get d answer
viole3t@valerie
4 years ago
i dnt understand any of the solution pls help
tenten
5 years ago
what a judicious question
ahmedhalidu
5 years ago
But this is not the actual questions we are 2 answered in jamb.no matrix,no integration,no co odinate geometry?
Remmy2
4 years ago
Trying very hard to understand the question n the answer,, still to no avail,,, i love learning pls make it easy for people like me thanks
ruthbaiby
3 years ago
the answer is c ; be it -25/4 or -13/2
Yaks SG
3 years ago
Laughing data

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is this really jamb pst questions?
prof kc