dc123 wrote:
What is the value of a^-2b^-3
1) a^-3b^-2 = 36^-1
2) ab^-1 = 6^-1
the Ans says C but doesnt only B work?
What is \(a^{-2}b^{-3}=\frac{1}{a^2b^3}=\frac{1}{(ab)^2b}\)
1) a^-3b^-2 = 36^-1
\(a^{-3}b^{-2} = 36^{-1}\)
\(\frac{1}{a^3b^2} = \frac{1}{36}\)
\(\frac{1}{a^3b^2} = \frac{1}{36}\)
\(\frac{1}{(ab)^2a} = \frac{1}{36}\)
\(\frac{1}{(ab)^2} = \frac{a}{36}\)
\(\frac{1}{(ab)^2b}=\frac{a}{36b}\)
--------------------1\(a^3b^2=36\)
Possible values of a and b;
\(a=1; b=6\)
\(a=2; b=\sqrt{\frac{36}{8}}\)
\(a=0.1; b=\sqrt{\frac{36}{0.001}}\)
Not Sufficient.
2) ab^-1 = 6^-1
\(ab^{-1} = 6^{-1}\)
\(\frac{a}{b} = \frac{1}{6}\)
------------------------2a=1; b=6
a=2; b=12
a=3; b=18
a=3.2; b=19.2
Not Sufficient.
Combining both and using 1 and 2:
\(\frac{1}{(ab)^2b}=\frac{a}{36b}=\frac{1}{36*6}=\frac{1}{216}\)
Sufficient.
Ans: "C"
_________________