Of the following expressions the one equal to a^-1b^-1a^-3 - b^-3 is:

a^-1b^-1a^-3 - b^-3 = 1ab1a^3-1b^3 = 1ab1a^3-1b^3a^3b^3a^3b^3 = a^2b^2b^3-a^3, a^2b^2b^3 - a^3.

smc

algebra intermediate

Problem

Of the following expressions the one equal to

\frac{a ^{- 1} b ^{- 1}}{a ^{- 3} - b ^{- 3}}

is:

(A)

\frac{a ^{2} b ^{2}}{b ^{2} - a ^{2}}

(B)

\frac{a ^{2} b ^{2}}{b ^{3} - a ^{3}}

(C)

\frac{ab}{b ^{3} - a ^{3}}

(D)

\frac{a ^{3} - b ^{3}}{ab}

Solution

\frac{a ^{- 1} b ^{- 1}}{a ^{- 3} - b ^{- 3}} = \frac{\frac{1}{ab}}{\frac{1}{a ^{3}} - \frac{1}{b ^{3}}} = \frac{\frac{1}{ab}}{\frac{1}{a ^{3}} - \frac{1}{b ^{3}}} \cdot \frac{a ^{3} b ^{3}}{a ^{3} b ^{3}} = \frac{a ^{2} b ^{2}}{b ^{3} - a ^{3}}

\frac{a ^{2} b ^{2}}{b ^{3} - a ^{3}}

Final answer