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Unformatted text preview: ed to know for combining exponents by multiplication or division. First, you can combine base numbers first, but only if the exponents are the same: ax · bx = (ab)x
ax a = bx b x 2 multiply 2 by itself twice: 23 = 2 · 2 · 2 = 8. In the number 2 , the base number is 3 and the exponent is 4. To () 4 2 ()
3 4 () 4 Second, you can combine exponents first, but only if the base numbers are the same. When multiplying these terms, add the exponents. When dividing them, subtract the denominator exponent from the numerator exponent: ax · ay = a (x + y)
ax = a( x − y) ay When the same base number (or term) appears in both the numerator and denominator of a fraction, you can www.petersons.com Numbers and Operations, Algebra, and Functions 251 factor out, or cancel, the number of powers common to both. Example: Which of the following is a simplified version of (A) (B) (C) (D) (E) Solution: The correct answer is (A). The simplest approach to this problem is to cancel, or factor out, x2 and y2 from numerator and denominator. This leaves you with x1 in the denominator and y1 in the denominator. You should also know how to raise exponential numbers to powers, as well as how to raise base numbers to negative and fractional exponents. To raise an exponential number to a power, multiply exponents together:
y x x y 1 xy
x 2 y3 ? x 3 y2 1 x5y5 (a )
x y = a xy Raising a base number to a negative exponent is equivalent to 1 divided by the base number raised to the exponent’s absolute value:
a− x = 1 ax To raise a base number to a fractional exponent, follow this formula:
a y = ax
x y Also keep in mind that any number other than 0 (zero) raised to the power of 0 (zero) equals 1: a0 = 1 [a ≠ 0] Example: (23)2 · 4–3 = (A) 16 (B) 1 (C) (D) (E) Solution: The correct answer is (B). (23)2 · 4–3 = 2(2)(3) ·
1 = 26 = 26 = 1 4 3 4 3 26
2 3 1 2 1 8 www.petersons.com 252 Chapter 15 Exercise 4
Work out each problem. For questions 1–4, circle the letter that appears before your answer. Question 5 is a gridin question. 1.
a2 b ÷ a2c = b 2 c bc 2 1 (A) a 1 (B) b b (C) a c (D) b 4. If x = –1, then x–3 + x–2 + x2 + x3 = (A) –2...
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This note was uploaded on 08/15/2010 for the course MATH a4d4 taught by Professor Colon during the Spring '10 term at Embry-Riddle FL/AZ.
- Spring '10