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EXPONENT RULES & PRACTICE 1. PRODUCT RULE: To multiply when two bases are the same, write the base and ADD the exponents. Examples: A. B. C. 2. QUOTIENT RULE: To divide when two bases are the same, write the base and SUBTRACT the exponents. Examples: A. B. ˘ C. ˇ ˇ 3.
Exponents and Order of Operations. Notes, Examples, and Exercises (with Solutions) Topics include PEMDAS or GEMDAS, exponent laws, square roots, and more.
Your answer should contain only positive exponents. 1) 42 ⋅ 42 2) 4 ⋅ 42 3) 32 ⋅ 32 4) 2 ⋅ 22 ⋅ 22 5) 2n4 ⋅ 5n4 6) 6r ⋅ 5r2 7) 2n4 ⋅ 6n4 8) 6k2 ⋅ k 9) 5b2 ⋅ 8b 10) 4x2 ⋅ 3x 11) 6x ⋅ 2x2 12) 6x ⋅ 6x3-1- ©b h2a0 F1r2 G 7K wuct va3 hSdoLfrt ew ia wrne u hLpL4C X.O f rA Hlzl N Cr7icg9hEtHsS Krdexs ue 0r Rvqegd i.o s ...
All of the rules for manipulating exponents may be deduced from the laws of multiplication and division that you are already familiar with. Exponential notation. Repeated multiplication is represented using exponential notation, for example: 3 · 3 · 3 · 3 = 34. There are four factors in the product, each of which is a 3.
The exponent laws are the tools needed for working with expressions involving exponents. They are stated precisely below, and then discussed in the para-graphs that follow. EXPONENT LAWS. xmxn = xm+n. = xmn xn. (xm)n = xmn. (xy)m = xmym. x xm. ( )m = y ym. Let x , y , m and n be real numbers, with the following exceptions:
You have seen that exponential expressions are useful when writing very small or very large numbers. To perform operations on these numbers, you can use properties of exponents.
Correct rules: (a+b)2 = a2 + 2ab + b2 , (a + bI3 = a3 + 3a2 b + 3a b2 + b3 , etc.; see Section D 9. Exponentiation precedes m~ltiplicatior~. For example, 7a3 = 7.a.a.a , (7a)3 , which would be 7a.7a.7a = 7 3 a 3 . 10. (-a)n = (-IInan = an if n even -an if n odd e.g. (-x)~ = (-x)(-X) = (-I(-)x2 = x2 (-x)3 = (-x)(-x)(-x) = (-)(-)(-)x 3--3 - X
