1 / 7

Negative and rational exponents

Negative and rational exponents. =. =. 1. 1. 1. 1. b × b. b × b × b × b. b × b. x n. b 2. b 2. x – n =. Look at the following division:. b 2 ÷ b 4 =. Negative exponents. 1. Write an equivalent expression for the term using the division law for exponents. b 2.

rogercollins
Download Presentation

Negative and rational exponents

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Negative and rational exponents

  2. = = 1 1 1 1 b × b b × b × b × b b × b xn b2 b2 x–n= Look at the following division: b2 ÷ b4 = Negative exponents 1 Write an equivalent expression for the term using the division law for exponents. b2 Using the exponent law xm÷xn= x(m– n) b2 ÷ b4 = b(2 – 4) = b–2 This means that b–2 = In general,

  3. Reciprocals 1 a b The reciprocal of a is a b a The reciprocal of is x-1 We can find reciprocals on a calculator using the key. A nonzero number raised to the power of –1 gives us the reciprocalof that number. The reciprocal of a number is what we multiply the number by to get 1.

  4. Annual or monthly interest Riley puts $1000 in a savings account. The first $100 does not gather interest and the rest earns interest at 3.5% per year. Write a function for Riley’s total savings after t years. What is the equivalent monthly interest rate? Rewrite the function using this rate. f(t) = 100 + 900(1.035)t The annual interest rate, 1.035, is the monthly rate (m) multiplied by itself 12 times. This means that 1.035 = m12. f(t) = 100 + 900(m12)t m= 1.0351/12 f(t) = 100 + 900(m)12t The monthly rate is 0.29%. f(t) = 100 + 900(1.0351/12)12t ≈ 100 + 900(1.0029)12t

  5. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 3 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 9 × 9 Suppose we have 9 . What is the value of ? Using the exponent law, 91 = 9 9×9= 9+= Rational exponents But also, 9 × 9 = 3 × 3 = 9 The square root of x. So in general, x = x Suppose we have 8 . What is the value of 8×8 ×8 ? 8 + + = 81 = 8 Using the exponent law, 8×8 ×8 = But also, 8 × 8 × 8 = 2 × 2 × 2 = 8 3 3 3 The cube root of x. So in general, x = x 3

  6. 1 n m n n x = x In general, Can you find a rule for expressions in the form x ? Rational exponents m 1 We can write x as x ×m n n and we know that (xm)n=xmn, 1 1 n x × m= (x)m = ( x )m therefore, n n m 1 Also, we can write x as xm× n n 1 1 n therefore, x = (xm) = xm n n m × m m or n n In general, x = xm x = (x )m n n

  7. 3 3 2 2 m m n n What is the value of 25 ? or n n In general, x = xm x = (x )m Rational exponents So using the 2nd rule we can write: 25 is a perfect square so it is easiest to use the rule where we square root first, then cube. 25 = (25) 3 = (5)3 = 125 Notice that the numerator of the fraction determines the powerand the denominator determines the degree of the root.

More Related