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Mathematics
Problem
A student begins a proof of the negative rational exponent rule for
a
>
0
a>0
a
>
0
as follows:
a
0
a
3
/
2
=
a
0
−
3
2
=
a
−
3
2
.
\frac{a^{0}}{a^{3/2}} = a^{0-\frac{3}{2}} = a^{-\frac{3}{2}}.
a
3/2
a
0
=
a
0
−
2
3
=
a
−
2
3
.
Which of the following substitutions for
a
0
a
3
/
2
\dfrac{a^{0}}{a^{3/2}}
a
3/2
a
0
is necessary to complete the proof that
a
−
3
2
=
1
a
3
/
2
a^{-\frac{3}{2}}=\dfrac{1}{a^{3/2}}
a
−
2
3
=
a
3/2
1
? a)
a
3
/
2
a^{3/2}
a
3/2
b)
1
1
1
c)
1
a
3
/
2
\dfrac{1}{a^{3/2}}
a
3/2
1
d)
a
3
a^{3}
a
3
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