Rational exponents evaluate each expression. (a) 27^(1/3) (b) (-8)^(1/3) (c) -(1/8)^(1/3)

Khaleesi Herbert 2020-10-27 Answered

Rational exponents evaluate each expression.
(a) 271/3
(b) (8)1/3
(c) (18)1/3

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Expert Answer

d2saint0
Answered 2020-10-28 Author has 89 answers
(a) Definition used:
Definition of rational exponents:
"For any rational exponent m/n in its lowest terms, where m and n are integers and n>0 we define, (a)mn=(a)mn=(an)m.
Formula used:
Laws of exponents:
"To raise a power to a new power, multiply the exponents".
(am)n=amn
Calculation:
The given expression is 2713.
Use the above mentioned definition and simplify the expression as shown below.
2713=(3×3×3)13
=(33)13
=33×13
=3
Thus, the value of the expression 2713 is 3.
(b) Use the above definition and formula mentioned in sub part (a) and simplify the expression as shown below.
(8)13=((2)×(2)×(2))13
=(2)3×13
=(2)3×13
= 2
Thus, the value of the expression (8)13 is (-2).
(c) Use the above definition and formula mentioned in sub part (a) and simplify the expression as shown below.
(18)13=(123)13
=(23)13
=(23×13)
On further simplifications, the following is obtained.
(18)13=(21)
=(12)
Thus, the value of the expression (18)13 is =(12).
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