19
Square, cube and power of a number
Textbook: Part 1, lesson 19, pp. 74–77
GoalKnow the square, cube and power of a number; evaluate expressions with powers.
New words
square · kvadratcube · kubpower · darajaexponent · daraja ko‘rsatkichi
Explanation
The product a · a is written a² and read “a squared”; a · a · a is a³, “a cubed”. A product of n equal factors is written aⁿ: a is the base, n is the exponent, and aⁿ is the n-th power of a. The first power equals the number itself: a¹ = a, and the exponent 1 is usually not written. For example 12² = 12 × 12 = 144, 6³ = 6 × 6 × 6 = 216, 2⁵ = 32. A power is not 2 × 5: it means multiplying 2 by itself 5 times. If an expression has powers, calculate them first, then do the other operations.
Worked examples
12² = 144; 2⁵ = 2 × 2 × 2 × 2 × 2 = 32; 10³ = 1 000.
(3 + 2)² × 4 − 2³ = 25 × 4 − 8 = 100 − 8 = 92. First the bracket and powers, then multiplication, then subtraction.
Class activity
“Power table”: pupils fill in a table of squares and cubes of 1 to 10, then use it to find n in n² = 81 or n³ = 343.
Practice
1
Find the value of 7² + 3³.
76
2
Compute 2⁶.
64
3
Find the root of y · y · y = 125.
5
4
Are 3² and 3 × 2 the same? Why?
No: 3² = 3 × 3 = 9 but 3 × 2 = 6. A power multiplies the base by itself as many times as the exponent says.