Lesson 4-2 Warm-Up

Exponents (4-2) What is a a “base” number, “exponent” , and “power”? exponent: a shorthand way to show repeated multiplication of a base number by showing how many times to multiply the base number by itself using a superscript (a little number at the top right of the base number) power: includes both the base number and the exponent (For example, you read 54 as “five to the fourth power” and 57 as “five to the seventh power”. Note: Exponents of 2 and 3 have special names – “squared” and “cubed”. For example, 52 is read as “five squared” and 53 is read as“five cubed”.

Exponents (4-2) How do you read and simplify an exponent? Read an expression containing an exponent as, “(base number) to the (value of the exponent) power.”

Exponents (4-2) How do you write an number in exponential form? How do you evaluate an expression containing one or more exponent? To write a number using an exponent, write a number or letter that is repeatedly multiplied by itself only one time with an exponent (power) indicating the number of time the multiplication is repeated. Example: (-5)(-5)(-5) = (-5)3 Example: -2 • a • b • a • a = -2 • a • a • a • b = -2a3b a • a • a = a3 To evaluate an expression containing an exponent: 1. substitute the variables (if you know what they equal), and 2. use the order of operations PEMDAS (the “E” stands for Exponents, so exponents are done after grouping symbols) Example: Simplify 4(3.7 + 2)2 . Example: Simplify -2x3 + 4y, for x = 2 and y = 3.

Include the negative sign within parentheses. Exponents LESSON 4-2 Additional Examples Write using exponents. a. (–11)(–11)(–11)(–11) (–11)4 Include the negative sign within parentheses. b. –5 • x • x • y • y • x –5 • x • x • x • y • y Rewrite the expression using the Commutative and Associative Properties. –5x3y2 Write x • x • x and y • y using exponents.

Many animals became trapped at the La Brea Tar Exponents LESSON 4-2 Additional Examples Many animals became trapped at the La Brea Tar Pits in California during the last ice age. The ice age ended about 104 years ago. How many years ago was this? 104 = 10 • 10 • 10 • 10 The exponent indicates that the base 10 is used as a factor 4 times. = 10,000 years Multiply. The last ice age ended about 10,000 years ago.

Work within parentheses first. Exponents LESSON 4-2 Additional Examples a. Simplify 3(1 + 4)3. 3(1 + 4)3 = 3(5)3 Work within parentheses first. = 3 • 125 Simplify 53. = 375 Multiply. b. Evaluate 7(w + 3)3 + z, for w = –5 and z = 6. Replace w with –5 and z with 6. 7(w + 3)3 + z = 7(–5 + 3)3 + 6 = 7(–2)3 + 6 Work within parentheses. = 7(–8) + 6 Simplify (–2)3. = –56 + 6 Multiply from left to right. = –50 Add.

= 68 – 42 Add and Subtract in order from left to right. Exponents LESSON 4-2 Additional Examples Simplify 32 + 62 – 14 • 3. 32 + 62 – 14 • 3 = 32 + 36 – 14 • 3 Exponent: 62 = 6 • 6 = 36. = 32 + 36 – 42 Multiply 14 and 3. = 68 – 42 Add and Subtract in order from left to right. = 26 Add and Subtract in order from left to right

Evaluate 5x + 32 ÷ p for x = 2 and p = 3. Exponents LESSON 4-2 Additional Examples Evaluate 5x + 32 ÷ p for x = 2 and p = 3. 5x + 32 ÷ p = 5 • 2 + 32 ÷ 3 Substitute 2 for x and 3 for p. = 5 • 2 + 9 ÷ 3 Exponent (Power). = 10 + 3 Multiply and Divide from left to right. = 13 Add and Subtract from left to right.

Write using exponents. 1. x • y • z • x • z 2. a • b • b • b • 3 LESSON 4-2 Lesson Quiz Write using exponents. 1. x • y • z • x • z 2. a • b • b • b • 3 3. Simplify 5(2 + 4)2. 4. Evaluate (g3 – 7)2 • 5 + 4, for g = 3. x2yz2 3ab3 180 2,004