1 / 9

Aim: How do we solve equations with fractions, negative numbers, or variables in the exponents?

Aim: How do we solve equations with fractions, negative numbers, or variables in the exponents?. Do Now:.

leo-huffman
Download Presentation

Aim: How do we solve equations with fractions, negative numbers, or variables in the 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. Aim: How do we solve equations with fractions, negative numbers, or variables in the exponents? Do Now: Meteorologists use the formula D3 = 216T2 to describe the size and duration of storms. In the formula, D is the diameter of the storm in miles and T is the duration, or the number of hours the storm lasts. If the diameter of the thunderstorm is 12 miles, about how long would this storm last?

  2. Model Problem Meteorologists use the formula D3 = 216T2 to describe the size and duration of storms. In the formula, D is the diameter of the storm in miles and T is the duration, or the number of hours the storm lasts. If the diameter of the thunderstorm is 12 miles, about how long would this storm last? D3 = 216T2 substitute D = 12 123 = 216T2 simplify and solve 1728 = 216T2 8 = T2 square root of both sides T  2.8 hours

  3. Power of Power Property Power of Power Rule (am)n = am•n x1 = x (x2)1/2 = (x -1/2)-2 = x1 = x How do we use this power rule to solve equations like 2x -1/3 = 6 ? raise x -1/3 to the reciprocal power but first . . . .

  4. Power of Power Property isolate the variable with the exponent 2 2 multiply both sides by the exponent’s reciprocal simplify Using the Power of Power Rule (am)n = am•n but first . . . . 2x -1/3 = 6 x -1/3 = 3 (x -1/3)-3 = 3-3 x = 1/33 = 1/27 Check your answer

  5. Model Problem Solve for x3/2 + 1 = 9 x3/2 + 1 = 9 isolate variable with a coefficient of 1 -1 -1 x3/2 = 8 raise both members of equation by reciprocal power (x3/2)2/3 = 82/3 x = 82/3 simplify

  6. Rational Exponents containing variables Solve and check: 5x + 1 = 54 for b 0 and b  1, bx = by  x = y because the base on both sides of this equation is 5, we can write the following: x + 1 = 4 x = 3 check: 53 + 1 = 54 54 = 54

  7. change the right side to base 2 simplify equate exponents solve check: Rational Exponents containing variables Solve and check: 2x – 1 = 82 bx = by  x = y 2x – 1 = (23)2 23 = 8 2x – 1 = 26 x – 1 = 6 x = 7 27 – 1 = 82 26 = 82 64 = 64

  8. change both sides to base 2 simplify equate exponents solve check: Rational Exponents containing variables Solve and check: (2-2)x = (23)1 –x 1/4 = 2-2 8 = 23 2-2x= 23 – 3x -2x = 3 – 3x x = 3

  9. change both sides to base 3 simplify equate exponents solve check: Rational Exponents containing variables Solve and check: 9x + 1 = 27x (32)x + 1 = (33)x 32 = 9 33 = 27 32x + 2 = 33x 2x + 2 = 3x x = 2 92 + 1 = 272 93 = 272 729 = 729

More Related