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# Level 3-4 Algebra - Powers

Powers - the word makes you think of something important. And well it should. Powers are a major part of KS3 Maths, especially in the field of algebra. Powers are the small numbers that appear to the upper right of other numbers. Although small they can make a huge difference!

Powers are also known as indices or exponents. Whichever word you use, they all mean the same thing. Powers are an easy way to show that a number has been multiplied by itself. It's easy to write 2 x 2, or even 2 x 2 x 2. But when it comes to longer multiplications powers save both time and space!

How would you write the number 10 billion? Well, 10 billion is 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10,000,000,000. But, it's much easier and quicker to write 1010. This saves a lot of paper when writing out very large numbers!

1.
To what power does 6 need to be raised to give a value of 216?
2
3
4
5
63 = 6 x 6 x 6
2.
19 is 1. What is 91?
1
9
18
19
3.
If x = 2 and y = 8, what is the answer to 8y / x4?
2
4
8
16
Be careful not to mix up multiplying numbers together (as in 8y) when finding the value of numbers with powers (as in 24)
4.
In the equation x3 + y2 - 6 = 51, we are told that the value of x is 2. What is the value of y?
7 or -7
8 or -8
9 or -9
11 or -11
Experiment with different values for y until you find the correct answer
5.
111 - x3 = -105. What is the value of x?
3
6
9
12
6.
If a = 4 and b = 5, which of these is the largest value?
4a2
3b3
a + a + a + a
b + b + b + b + b + b + b + b + b + b + b + b
3b3 = 3 x 125 = 375
7.
If a2 = 25, what is the value of a4?
29
50
125
625
a must be 5. a4 therefore must be 5 x 5 x 5 x 5
8.
If a = 3 and b = 10, what is the difference between a4 and b2?
17
19
21
23
a4 = 3 x 3 x 3 x 3 = 81
9.
How would you work out the value of 36?
3 + 6
6 + 3
3 x 6
3 x 3 x 3 x 3 x 3 x 3
10.
Which of these gives the largest value?
4 + 6
4 x 6
46
64
64 = 1,296 whilst 46 = 4,096. We Googled it - did you?

Author:  Frank Evans