December 22, 2022

Bring food, fork, cup, plate for the luncheon please 

(enough for 3 to 4 people)

Part A: Exponents

 

2⁵ = 2 × 2 × 2 × 2 × 2

=32

 

6³ = 6 × 6 × 6

= 216

 

 

Expand the following.  Show your steps.

 

2⁴                                             5³                                             4⁴                                 10²

 

 

 

7³                                             3⁵                                             9²                                 8³                     

 

 

 

By definition, anything to the power 0 equals to 1.

e.g. 

Kwok⁰ = 1

 

 

Part B: Square roots

 

We can use square roots when we try to find the answer to a number for which two identical number multiply by each other.  For examples,

 

√49 = 7 because 7 x 7 = 49

 

Your calculator should have the square root function (√)

 

Find the square roots of the following numbers.  Use your calculator.

 

64          121         196         841         1369        2809

Part C: Applications of exponents and square roots

 

If the area for a square is 81cm², what is the length?

 

                  √81 = 9cm (The length is 9cm)

 

 

 

 

If the length for a square is 15cm, what is the area?

      

      15 x 15 or 15² = 225cm²

 

 

Calculate the length of these squares if the areas are:

 

      100cm²            169cm²      441cm²                   2601cm²

 

 

 

Calculate the area of these squares if the lengths are: Use exponents

 

      17.3cm            28.8cm      30.5cm            51.7cm

 

      

 

Basic order of operations with square roots and exponents

-   Step 1: calculate the exponents and square roots first

-   Step 2: then calculate the multiplication and division

 

e.g. 6² x 5³ x 1²                              5⁴ ÷ 5¹ x 2³

= 36 x 125 x 1                      = 625 ÷ 5 x 8

= 4500                              = 1000

 

 

Calculate

 

      9² x 3³ x 2²           4³ ÷ 2² x 3⁴          14² ÷ 2² x 2⁵         10² ÷ 5² x 2²