A student begins a proof of the negative rational exponent rule for as follows: a^ 0…

MATHEMATICS · Single correct · CBSE · Mathematics · Number Systems · Number Systems

Problem

A student begins a proof of the negative rational exponent rule for

a>0

as follows:

\frac{a^{0}}{a^{3/2}} = a^{0-\frac{3}{2}} = a^{-\frac{3}{2}}.

Which of the following substitutions for

\dfrac{a^{0}}{a^{3/2}}

is necessary to complete the proof that

a^{-\frac{3}{2}}=\dfrac{1}{a^{3/2}}

? (a)

a^{3/2}

(b)

1

(c)

\dfrac{1}{a^{3/2}}

(d)

a^{3}