Pre-Algebra Powers and Exponents

What Are You Learning? I CAN write powers as a product of the same factor and I CAN write products in exponential form. I CAN evaluate exponents.

Why Do You Need To Know This? Exponents are used in the real-world to represent extremely large and small numbers. They are also used in solving problems.

Vocabulary Words Factors—Two or more numbers multiplied together to form a product. Example—2 • 3 = 6 The numbers 2 and 3 are factors.

Vocabulary Exponent—Number that tells how many times the base is used as a factor. 4²--2 is the exponent and it shows that 4 will be multiplied two times. 4 • 4

Vocabulary Base—The common factor or number being multiplied. 5 • 5 • 5 • 5 • 5 Five is the base

Vocabulary Powers—Numbers expressed using exponents 4² and 6³ are examples of powers. 4² is read “four to the second power.” 6³ is read “six to the third power.”

Vocabulary Squared—A number multiplied by itself two times. 4 x 4 or 4² The four is being squared. Cubed—A number multiplied by itself three times. 2 x 2 x 2 or 2³

Write Numbers in Exponential Form Exponential Form—Numbers written with exponents. Example 1—Write (-5)(-5)(-5) in exponential form. -5 is the base. It is used as a factor 3 times. So, the exponent is 3. (-5)(-5)(-5) = (-5)³

Write each expression in exponential form. 6 · 6 · 6 (-3)(-3)(-3)(-3) (-4n)(-4n)(-4n)(-4n)(-4n) 4 · y · x · y · 3 · x · y 9 · (p + 1)(p +1) -5 · x · x · y · y · x (a + 1)(a +1)(a +1)

Write each expression in exponential form. -8 • n • n • n • 4 • t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Vocabulary Evaluate—Find the value of an expression. Standard Form—Numbers written without exponents.

Write Powers in Standard Form Evaluate each expression. Example 1 -- 2 to the fifth power = 2 · 2 · 2 · 2 · 2 = 32 Example 2-- 4³ = 4 · 4 · 4 = 64

Evaluate each expression. 7³ 52 (-4)³ -8² 3 · 4² 4² · 5³ 2³ · 5² · 7 3 · 5² + 2³ · 3²

Evaluate. -32 -9 9 6 -6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Evaluate each expression 5² · 8² · 3³ 9 · 6² · 2 · 3³ 3(2 • 2 + 5)² 6² + 2(6) + 5

Evaluate. 12 - 42 -4 12 – 4 • 4 4 12 - 16 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

4ab2 and 4(ab)2 (2x)³ and 8x³ (mn)4 and m4 • n4 c³d³ and cd³ Determine whether each pair of expression is equivalent. Write yes or no. 4ab2 and 4(ab)2 (2x)³ and 8x³ (mn)4 and m4 • n4 c³d³ and cd³

Compare using <, >, or =. 3³ 5² 4³ 8² 64÷8 2³ 4•10 102 -5³ -3° 35 4³ -10³ (-10)³ 5² 23 6³ 42 24 4²

Class Work