Core Connections Integrated II, 2015
CC
Core Connections Integrated II, 2015 View details
2. Section 6.2
Continue to next subchapter

Exercise 85 Page 353

Practice makes perfect
a When we have a power raised to a fraction you can rearrange this expression by writing the exponent as a product, and then pull out one of the factors as an exponent.
64^(2/3)
64^(1/3 * 2)
(64^(1/3))^2
Whenever you have a rational exponent with a numerator of 1, you can rewrite this as a radical where the fraction's denominator becomes the radical's index.
(64^(1/3))^2
(sqrt(64))^2
(sqrt(4^3))^2
4^2
16
b We will simplify the expression in Part B in a similar way as we did with the expression in Part A.
25^(5/2)
25^(1/2 * 5)
(25^(1/2))^5

a^(1/2)=sqrt(a)

(sqrt(25))^5
(sqrt(5^2))^5
5^5
3125
c We will simplify the expression in Part C in a similar way as we did with the expressions in previous parts.
81^(7/4)
81^(1/4 * 7)
(81^(1/4))^7
(sqrt(81))^7
(sqrt(3^4))^7
3^7
2187