Question

What’s is the index notation?

Answer 1

Given:

a) 3 × 3 × 3 × 3 × 3

b) 4 × 4 × 4 × 5 × 5

c) 9 × 7 × 9 × 9 × 7 × 9

To find:

The index notation.

Solution:

a) Using multiplication rule of indices:

$a^{n} \times a^{m}=a^{n+m}$

$3\times3\times3\times3\times3=3^{1+1+1+1+1}$

                           $=3^5$

Therefore, $3\times3\times3\times3\times3=3^{5}$

b) Using multiplication rule of indices:

$4\times4\times4\times5\times5=4^{1+1+1}5^{1+1}$

                          $=4^35^2$

Therefore, $4\times4\times4\times5\times5=4^{3}5^{2}$

c) Using multiplication rule of indices:

$9\times7\times9\times 9\times7\times9=9^{1+1+1+1}7^{1+1}$

                                 $=9^47^2$

Therefore, $9\times7\times9\times 9\times7\times9=9^{4}7^{2}$