Home » If b3 = a-2 and c(frac{1}{3}) = a(frac{1}{2})b, express c in terms of a

If b3 = a-2 and c(frac{1}{3}) = a(frac{1}{2})b, express c in terms of a

If b³ = a^-2 and c^(frac{1}{3}) = a^(frac{1}{2})b, express c in terms of a

A.
a^{-(frac{1}{2})}
B.
a^(frac{1}{3})
C.
a^(frac{3}{2})
D.
a^(frac{2}{3})

Correct Answer: Option A

Explanation

c^(frac{1}{3}) = a^(frac{1}{2})b
= a^(frac{1}{2})b x a^-2
= a^{-(frac{3}{2})}
= (c^(frac{1}{3}))³
= (a^{-(frac{3}{2})})^(frac{1}{3})
c = a^{-(frac{1}{2})}