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

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 = -(17/4).

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

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Contributions (65)

Ali Inuwa Tanko
7 years ago
Haha read hard n pray papa God day
6 years ago
From laws of indices a^x/a^y=x-y..

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


b^q=-9/4-4/1=-9-16/4 =-25/4








7 years ago
using the laws of indices u get the values of p=5/2, q=-25/4 and r=-17/4 then you solve p +2q which gives -10
3 years ago
Here is an explanation:

To solve this, it is simple though the question looks more complex.


(a^2 b^2 c)^3\4 divided by a^-1 b^4 c^5 equals to a^p b^q c^r.

First let's separate the question, let's put aside the equals to part, now

Multiply all the numerator through by the power of 3/4. You will get a^3/2 b^-9/4 c^3/4 after this, use law of indices to divide the numerator with the denominator so we have a^3/2 ÷ a^-1 b^-9/4 ÷ b^4 c^3/4 ÷ c^5 after using law of indices to solve it, you will get a^5/2 b^-25/4 c^-17/4. So after these we get our p,q,r by comparing the powers.

:. a^5/2 b^-25/4 c^-17/4 = a^p b^q c^r, so p = 5/2, q = -25/4 c = -17/4. So now P + 2Q = 5/2 + 2(-25/4) after solving this, you will get -10 which is the answer.

Thank you.

REF: Jamb, 1999
4 years ago
d question self is confusing
6 years ago
guys pls i reall need sombody to put me true all this thing, cus i do not understant
1 year ago
God help me in my exam
6 years ago
This seems hard but using the laws of indices, it'll look so freaking easy, that triumphant feelin you get when you solve something right :D
4 years ago
upgrade in the explanation skills.
5 years ago
thanks waldon
7 years ago
This question is really great.what you need to do 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.
6 years ago
after breaking it with the law indices u will get a^5/2 b^-25/4 c^-17/4 note: that the question ask for this p+2q=? knowing that a^p b^q c^r than fix in the value when p=5/2 and q=-25/4.in solving 5/2+2(-25/4)=-10 as the answer.
6 years ago
Dis site is very interesting but please ur questions is nt clearly seen,,i lv u.
rachel b michael
7 years ago
dnt even undastand d qstion
7 years ago
a^6/4b^-9/4c^3/4 for d numerator wen u multiply 3/4 For d denominator q^-1b^4c^5

Apply the law of indices u will gt a^10/4b^-25/4c^-17/4(In a^p b^q c^r)

but the questn is d value of p+2q i.e p=10/4 q=-25/4 Substitute it in p+2q so 10/4+2(-25/4)=10/4-50/4 =40/4=-10

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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