Exponents and Powers

Exponents and Powers

Exponential notation is a concise way to represent repeated multiplication. It involves two essential components: a base and an exponent.

Example: 104 = 10 × 10 × 10 × 10 = 10000

In this expression, the number 10 is the base and 4 serves as the exponent, index or power.

The base indicates the number that needs to be multiplied and the exponent, index or power signifies how many times the base is to be multiplied.

Note: When a negative number is raised to an even power, the result is always positive.

Example: (−7)² = (−7) × (−7) = 49

When a negative number is raised to an odd power, the outcome is always negative.

Example: (−7)³ = (−7) × (−7) × (−7) = −343

Laws of Exponents

For all non-zero integers 'a' and 'b' and whole numbers 'm' and 'n:

Note: ⇒  (1)^Odd = 1                                           
⇒ (1)^Even = 1
⇒ (−1)^Odd = −1                                        
⇒ (−1)^Even = 1

Example: Simplify the following expression using laws of exponents:

a) x⁴y⁻¹z
b) x⁴y⁻¹z³
c)  x⁴y⁻¹z⁶
d)  x⁴y⁻¹z⁹

Answer: d)  x⁴y⁻¹z⁹

Explanation: Using laws of exponents,

Standard Form of a Number

The standard form of a number is a representation where the number is expressed as the product of a decimal number between 1.0 and 10.0 (inclusive of 1.0) multiplied by a power of 10.

Example: The mass of Mars is 639000000000000000000000 kg. How is the mass of Mars expressed in standard form?        

a) 6.39 × 10¹⁹ kg
b) 6.39 × 10²¹ kg
c) 6.39 × 10²² kg
d) 6.39 × 10²³ kg

Answer: d) 6.39 × 10²³ kg

Explanation: