# Chapter 2 : Powers and Exponents

### Topics covered in this snack-sized chapter:

#### Power arrow_upward

• Power is the number of times a number or expression is multiplied by itself.
• Another name for power is index or exponent.
• Examples :
• 25 = 2 × 2 × 2 × 2 × 2 = 32
• (-4)3 = (-4) × (-4) × (-4) = -64
• 1n = 1 for any n, 0n = 0 for any n

#### Squares and Cubes arrow_upward

• bn is read as “b raised to the nth power”.
• b2 is read as “b squared”.
• b2 is always greater than 0 (positive) if b is not zero, since the product of two negative numbers is positive.
• b3 is read as “b cubed”.
• b3 can be negative or positive.
• The following table shows squares and cubes of numbers from 1 to 10:

•  Number Square Cube 1 12 = 1 13 = 1 2 22 = 4 23 = 8 3 32 = 9 33 = 27 4 42 = 16 43 = 64 5 52 = 25 53 = 125 6 62 = 36 63 = 216 7 72 = 49 73 = 343 8 82 = 64 83 = 512 9 92 = 81 93 = 729 10 102 = 100 103 = 1000

• If you raise a fraction, p/q, to a power, then
• Example:

• #### Exponent arrow_upward

• An exponent is used to show repeated multiplication.
• Where,
• a and nare integers.
• The integera is called the base andn is called the exponent.
• In the expression bn , b is called the base and n is called the exponent.
• In the expression 25 , 2 is the base and 5 is the exponent.

• #### Rules of Exponents arrow_upward

• The exponent says how many times to multiply the given number by itself.
• A negative exponent means divide.
• A fractional exponent like 1/n means to take the nth root:

•  Rules Example x1 = x 71 = 7 x0 = 1 80 = 1 x-1 = 1/x 4-1 = 1/4 xm xn = xm+n x3 x5 = x3+5 = x8 (xm )n = xmn (x4 )5 = x4×5 = x20 (xy)n = xn yn (xy)7 = x7 y7

#### Exponents: Properties arrow_upward

• Example: What is the value of 63 ?
• Solution: Since 6 = 3 × 2
•     = 27 × 8

= 216

#### Negative Exponents arrow_upward

• For any non-zero integer b,
•
• so
• Multiplying by b-n is same as dividing by bn .
• Example:
• Example: Find the value of ?
• Solution:

• #### Exponential Expansions arrow_upward

 Function Summation Expansion

#### Thank You from Kimavi arrow_upward

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