b The numerator of a rational exponent is the exponent of the expression, and the denominator is the index.
C
c A negative exponent in a numerator, or of an integer, will be moved to the denominator and become positive. A negative exponent in a denominator will be moved to the numerator and become positive.
D
d The numerator of a rational exponent is the exponent of the expression, and the denominator is the index.
A
a 25
B
b 4
C
c 1/4
D
d 1/3
Practice makes perfect
a To simplify the given expression, remember that the numerator of a rational exponent is the exponent of the expression, and the denominator is the index.
a^()1 n=sqrt(a) and a^() m n=sqrt(a^m)
Let's simplify the expression!
b To simplify the given expression, remember that the numerator of a rational exponent is the exponent of the expression, and the denominator is the index.
a^()1 n=sqrt(a) and a^() m n=sqrt(a^m)
Let's simplify the expression!
c We want to simplify the given number. Notice that this expression has a negative exponent. When this is the case, the expression can be moved to the denominator and the exponent will become positive.
a^(- mn)= 1/a^()mn ⇒ 16^(- 1/2)=1/16^(1/2)
We will split the base into perfect square factors to simplify this fraction. Because the denominator of the exponent is 2, this will allow us to simplify the rational exponent. Let's start!
d To simplify the given expression, remember that the numerator of a rational exponent is the exponent of the expression, and the denominator is the index.
a^()1 n=sqrt(a) and a^() m n=sqrt(a^m)
Let's simplify the expression!
