Question

6. If 2205 = (3)a x (5)b x (7)c
(i) find the numerical values of a, b and c.
(ii) Hence evaluate (3)a x (5)-b x (7)-c
NOTE: a,b and c are powers of that numbers..​

Answer 1

$\qquad$Given :

If 2205 = $\sf 3^a \times 5^b \times 7^c$

$\qquad$To find :

The numerical values of a, b and c. Hence evaluate $\sf 3^a \times 5^b \times 7^c$

$\qquad$ Solution :

Let's do prime factorisation of 2205

$\qquad$ 3|2205

$\qquad$ 3| 735

$\qquad$ 5| 245

$\qquad$ 7| 49

$\qquad$ 7| 7

$\qquad \:$ | 1

$\qquad \:$2205 = 3 × 3 × 5 × 7 × 7

$\qquad \:$2205 = 3² × 5 × 7²

Now, substitute the values

$\implies\sf 3^a \times 5^b \times 7^c$

• a = 2
• b = 1
• c = 2

$\\\implies\sf 3^2 \times 5^1 \times 7^2$

$\implies\sf 9 \times 5 \times 49$

$\implies\sf 2205$