a The exponent of the radicand is the numerator of the rational exponent. The index of the radical is the denominator of the rational exponent.
B
b The exponent of the radicand is the numerator of the rational exponent. The index of the radical is the denominator of the rational exponent.
C
c The exponent of the radicand is the numerator of the rational exponent. The index of the radical is the denominator of the rational exponent.
D
d The exponent of the radicand is the numerator of the rational exponent. The index of the radical is the denominator of the rational exponent.
A
a 10^()13
B
b 15^()12
C
c 18^()34
D
d 5^(- 12)
Practice makes perfect
a When rewriting a radical into exponential form, the exponent of the radicand is the numerator of the rational exponent, and the index of the radical is the denominator of the rational exponent.
sqrt(a)=a^()1 n and sqrt(a^m)=a^() m n
With this in mind, we can rewrite the given expression.
&sqrt(10) ⇔ 10^()1 3
b When rewriting a radical into exponential form, the exponent of the radicand is the numerator of the rational exponent, and the index of the radical is the denominator of the rational exponent.
sqrt(a)=a^()1 n and sqrt(a^m)=a^() m n
Recall that a square root is a root with an index of 2. With this in mind, we can rewrite the given expression.
&sqrt(15) ⇔ 15^()1 2
c When rewriting a radical into exponential form, the exponent of the radicand is the numerator of the rational exponent, and the index of the radical is the denominator of the rational exponent.
sqrt(a)=a^()1 n and sqrt(a^m)=a^() m n
With this in mind, we can rewrite the given expression.
&sqrt(18)^3 ⇔ (18^()1 4 )^3
Now, let's simplify this expression as much as possible.
d When rewriting a radical into exponential form, the exponent of the radicand is the numerator of the rational exponent, and the index of the radical is the denominator of the rational exponent.
sqrt(a)=a^()1 n and sqrt(a^m)=a^() m n
Recall that a square root is a root with an index of 2. With this in mind, we can rewrite the given expression.
&1/sqrt(5) ⇔ 1/5^()1 2
If a power is in the denominator of a fraction with the numerator 1, it can be written as a power with a negative exponent. Using this property, we can simplify our expression completely.
&1/5^(12) ⇔ 5^(- 12)
