Question

(8x³y)²x√81x⁴y²÷(x³y²)²=2a3bxcyd​

Answer 1

Step-by-step explanation:

Given :-

[(8x³y)²×√(81x⁴y²)]/(x³y²)² = 2^a3^bx^cy^d

To find :-

Find the values of a ,b, c and d ?

Solution :-

Given that :

[(8x³y)²×√(81x⁴y²)]/(x³y²)² = 2^a3^bx^cy^d

On taking LHS

=>[(8x³y)²×√(81x⁴y²)]/(x³y²)²

8 can be written as 2×2×2 = 2³

81 can be written as 3×3×3×3 = 3⁴

=> [(2³x³y)²×√(3⁴x⁴y²)]/(x³y²)²

=> [(2³)²(x³)²(y)²×√(3⁴x⁴y²)]/(x³y²)²

Since (ab)^m = a^m × b^m

=> [2⁶x⁶y²×√(3⁴x⁴y²)]/(x³y²)²

=> [2⁶x⁶y²×√({3²x²y}²)]/(x³y²)²

=> [2⁶x⁶y²×(3²x²y)]/(x⁶y⁴)

Since (a^m)^n = a^(mn)

=> (2⁶×x⁶×y²×3²×x²×y/(x⁶y⁴)

=> (2⁶×3²×x⁶×x²×y²×y)/(x⁶y⁴)

=> (2⁶×3²×x⁸×y³)/(x⁶y⁴)

Since a^m × a^n = a^(m+n)

=>2⁶×3²×(x⁸-⁶)×(y³-⁴)

Since a^m/a^n = a^(m-n)

=> 2⁶×3²×x²×y-¹

Now,

2⁶×3²×x²×y-¹ = 2^a 3^b x^c y^d

On Comparing both sides then

a = 6

b = 2

c = 2

d = -1

Answer:-

The value of a = 6

The value of b = 2

The value of c = 2

The value of d = -1

Used formulae:-

• a^m × a^n = a^(m+n)

• a^m / a^n = a^(m-n)

• (a^m)^n = a^(mn)

• (ab)^m = a^m × a^n

Answer 2

Answer:

tennetiraj sir please answer my question