Question

Prove that the value of the expression: 36^5–6^9 is divisible by 30

Answer 1

36^5-6^9÷30

3^6-6^9

= 50,388,480

=50, 388,480÷30

= 50,388,480

Answer 2

Answer:

Step-by-step explanation:

To prove,

36⁵–6⁹ is divisible by 30

Recall the identities

(xᵃ)ᵇ = xᵃᵇ

xᵃ⁺ᵇ = xᵃ × xᵇ

Solution:

LHS = 36⁵–6⁹

We have 36 = 6², substituting in the above equation we get

36⁵–6⁹ = (6²)⁵–6⁹

Applying the identity (xᵃ)ᵇ = xᵃᵇ we get

(6²)⁵–6⁹ = 6¹⁰–6⁹

Applying the identity xᵃ⁺ᵇ = xᵃ × xᵇ

Taking the common factor 6⁹ outside we get

6¹⁰–6⁹ = 6⁹⁺¹–6⁹

= 6⁹×6¹–6⁹

= 6⁹(6 -1)

= 6⁹×5, is divisible by 6 (Since $\frac{6^9X5}{30} = \frac{6^9X5}{6X5} = 6^8$)

Since 6⁹×5 is divisible by 30, we have 36⁵–6⁹ is divisible by 30

Hence proved

#SPJ2