In mathematics there are instances when a number has to be multiplied

repeatedly and written.

In the lesson on factors you wrote 16 = 4 × 4

In the same manner we can write 16 = 2 × 2 × 2 × 2

There is a method of writing a number which is multiplied repeatedly

as above in a concise way.

When a number which is multiplied repeatedly is written in the above

manner in a concise way, we say that it is written using indices or that

it is written in index form.

The fact that 2 is multiplied three times over in this product is indicated

by the small digit 3 written at the top, on the right hand side of 2.

(1) Fill in the blanks in the following table.

(2) Write down using index notation, each of the following numbers

which has been expressed as a product. Find also the value of each

product.

(i) 5 × 5 

(ii) 10 × 10 × 10

(iii) 3 × 3 × 3 

(iv) 1 × 1 × 1

(v) 1 × 1 × 1 × 1 × 1 

(vi) 7 × 7 × 7 × 7

(vii) 5 × 5 × 7 × 3 × 3 

(viii) 6 × 3 × 3 × 3 × 4 × 4

(3) Write each of the following numbers which has been expressed

in words, in index form and as a product, and then write down its

value.

(i) Two to the power two 

(ii) Four cubed

(iii) Six squared 

(iv) Three to the power four

(v) Two to the power six 

(vi) Three cubed

To express the number 16 as a power of 2, it is necessary to know how

many times 2 should be multiplied by itself to obtain the value 16.

It is easy to use division to find the number of times a particular number

should be multiplied to obtain a given number. In the above example,

when the base is identified as 2, to find the index, the number 16 should

be divided repeatedly by 2.

(1) (i) What is two times 5 equal to?

(ii) What is 5 to the power two equal to?

(2) (i) What is three times 4 equal to?

(ii) What is 4 to the power three equal to?

(3) Write 32 as a power of 2.

(4) Write 144 as a power of 12.

(5) Write down 64

(i) as a power of 2.   (ii) as a power of 4.   (iii) as a power of 8.

(6) Write down 81

(i) as a power of 3. (ii) as a power of 9.

(7) Indicate the truth/falsehood of the following statements.

(2) Write down the following products using index notation.

(i) 5 × 5 × 5 × 5 

(ii) 4 × 4 × 7 × 7 × 7

(iii )3 × 3 × 3 × 3 ×3 × 8 

(iv) 2 × 2 × 2 × 3 × 3 × 5

(v) 4 × 4 × 4 × 5 × 7 × 7 × 7 × 7 

(vi) 2 × 3 × 3 × 2 × 5 × 2 × 3 × 5

(3) Find the value of each of the following expressions.

(5) Write down 256

(i) as a power of 2. (ii) as a power of 4. (iii) as a power of 16.

(6) Write down 729

(i) as a power of 3. (ii) as a power of 9. (iii) as a power of 27.

(7) Fill in the blanks appropriately with either the symbol “<” or the

symbol “>”.