Core Connections Integrated II, 2015
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Core Connections Integrated II, 2015 View details
1. Section 9.1
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Exercise 34 Page 494

Practice makes perfect
a Notice that the exponent of the given fraction is negative. When this is the case, the denominator can be switched with the numerator and the exponent will become positive.
(1/a)^(- mn)=a^()mn ⇒ (1/16)^(- 14)=16^(14) To simplify this fraction we will split the base into perfect fourth power factors. Because the denominator of the exponent is 4, this will allow us to simplify the rational exponent. Let's start!
16^()14
(2*2*2*2)^()14
(2^4)^()14
2^(4* 14)
2^1
2
b To simplify the given expression we will use the Properties of Rational Exponents. Remember that when you have a negative exponent of an integer you can move it to the denominator and change the exponent into a positive number. Let's do it!
x^(-1)y^(-3)
1/x^1* 1/y^3
1/x^1y^3
1/xy^3
c To simplify the given expression we will use the Properties of Rational Exponents. For this exercise, we will begin by distributing the exponents to each term inside the parentheses. Let's do it!
(25x^4)^(12)
25^(12)(x^4)^(12)

a^(12)=sqrt(a)

sqrt(25)sqrt(x^4)
â–Ľ
Simplify
sqrt(25)sqrt(x^(2*2))
sqrt(25)sqrt((x^2)^2)
5x^2