Exercise 134 Page 696

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.

(18^()14 )^3

PowPow

(a^m)^n=a^(m* n)

18^(14 * 3)

MoveRightFacToNumOne

1/b* a = a/b

18^()34

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)