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SAT/ACT MATH UNIT 2

SAT/ACT MATH UNIT 2. Powers and Roots. Definitions. Exponents – repeat multiplication of the same number. The exponent tells the number of times a number should be multiplied by itself. Base – the number that is being multiplied repeatedly. Meaning of Exponent. Exponent. Base. Important.

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SAT/ACT MATH UNIT 2

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  1. SAT/ACT MATH UNIT 2 Powers and Roots

  2. Definitions • Exponents– repeat multiplication of the same number. The exponent tells the number of times a number should be multiplied by itself. • Base – the number that is being multiplied repeatedly

  3. Meaning of Exponent Exponent Base

  4. Important • When a number or variable appears without an exponent, the exponent is understood to be 1. • Ex. 3 = 31

  5. Laws of Exponents • When multiplying powers with the same nonzero base, add their exponents. • When dividing powers with the same nonzero base, subtract their exponents. • To raise a power to another power, multiply the exponents.

  6. Example

  7. Order of Operations • P: First, evaluate expressions within Parentheses • E: Then evaluate Exponents • M: Next, Multiply and • D: Divide, working from left to right • A: Finally, Add and • S: Subtract, again working from left to right

  8. Square and Cube Root Radicals • Square = product of a number and itself • Square root – nonnegative number found by reversing the process of squaring • Radical – square root sign • Radicand – number underneath the radical

  9. Square and Cube Root Radicals • Cube root = finding the number that must be multiplied by itself 3 times to the radicand • Perfect Square – a whole number that has a whole number as a square root.

  10. Properties of Square Root Radicals

  11. Examples A If x = 32 – 16 ÷ 2 x 4, then x = (A) 0 (B) 2 (C) 4 (D) 8 (E) 32

  12. Examples B

  13. Examples D If b3 = 4, then b6 = (A) 2 (B) 8 (C) 12 (D) 16 (E) 64

  14. Examples B If w is a positive number and w2 = 2, then w3 = (A) √2 (B) 2√2 (C) 4 (D) 3√2 (E) 6

  15. Examples D

  16. Examples E Given y=wx2 and y is not 0. If the values of x and w are each doubled, then the value of y is multiplied by (A) 1 (B) 2 (C) 4 (D) 6 (E) 8

  17. Examples B If √n is a positive integer, how many values of n are in the interval 100 < n < 199? (A) three (B) four (C) five (D) six (E) seven

  18. Examples D (A) 3 (B) 6 (C) 9 (D) 27 (E) 81

  19. Examples E

  20. Examples A (A) I only (B) II only (C) I and III (D) II and III (E) I, II, and III

  21. Examples B

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