Exponents


 * __Exponents__

Topic Overview:** An algebraic expression is in simplest form when it is written with only positive exponents. If the expression is a fraction in simplest form, the only common factor of the numerator and denominator is 1. In the first property, which is the zero property, for every nonzero number //a//, //a//^0=1. In the second property, which is negative exponents, for every nonzero number //a// and integer //n//, //a^-n =// 1///a^n//. When you evaluate an exponential expression, you can write the expression with positive exponents before substituting values. A biologist uses exponents when studying green peach aphids. 1.** **Scientific Notation:** written as the product of two factors in the form //a x 10^n//, where //n// is an integer and 1 __<__ //a// < 10. 1.** 4yx^ -3 = 4y(1/x^3) = 4y/x^3 1.** Evaluate the expression for w = -3. Then describe what the value of the expression represents in the situation. 1000 x 2^w = 1000 x 2^-3 = 1000 x 1/8 = 125 There were 125 aphids 3 weeks before the present population of 1000 insects. 1. http://www.sosmath.com/algebra/algebra.html 2. http://www.algebrahelp.com/
 * Key Terms:
 * 2. Geometric Sequence:** multiplying the term in the sequence by a fixed number to find the next term.
 * 3. Common Ratio:** the fixed number
 * 4. Exponential Function:** a function in the form //y = a x b^x//, where //a// is a nonzero constant, //b// is greater than 0 and not equal to 1, and //x// is a real number.
 * 5. Exponential Growth:** can be modeled with the function //y = a x b^x// for //a// > 0 and //b// > 1
 * 6. Growth Factor:** the base, which is greater than 1.
 * 7. Compound Interest:** when a bank pays interest on both the principal and the interest an account has already earned.
 * 8. Interest Period:** the length of time over which interest is calculated.
 * 9. Decay Factor:** the base, which is between 0 and 1.
 * Examples:
 * 2.** 7(4 x 10^5) = (7 x 4) x 10^5 = 28 x 10^5 = 2.8 x 10^6
 * 3.** 11^4 x 11^3 = 11^4+3 = 11^7
 * 4.** a^6/a^14 = a^6-14 = a^-8 = 1/a^8
 * Word Problems:
 * Additional Links:

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