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 (62)

lucybaby2008
7 years ago
Both d questn nd d answer is nt clear 2 me.
Madoxsky
7 years ago
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Dagijoe
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
rachel b michael
7 years ago
dnt even undastand d qstion
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...
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...
Omotayo isaac
6 years ago
Is this what we want to solve in UTME......yea!I don suffer :(
Ali Inuwa Tanko
6 years ago
Haha read hard n pray papa God day
kingdomvic
6 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
Nabo Green
6 years ago
y is mathematics so simple for some pple,mehn i need thorough brushing up
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.
maxi957
6 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.
VITALISIBEKWE
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.
Saraphy
6 years ago
Lord help me in mathematic soln
emili
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

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