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

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d2saint0 · Accepted Answer

(a) Definition used:  Definition of rational exponents:  &quot;For any rational exponent m/n in its lowest terms, where m and n are integers and n&amp;gt;0 we define, (a)mn=(a)mn=(an)m.  Formula used:  Laws of exponents:  &quot;To raise a power to a new power, multiply the exponents&quot;.  (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  =−(2−3)13  =−(2−3×13)  On further simplifications, the following is obtained.  −(18)13=−(2−1)  =(−12)  Thus, the value of the expression −(18)13 is =(−12).

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

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