Question

If a/b = (-27/64)^3 ÷ (-3/4)^5 find the value of (a/b)^2​

Answer 1

Step-by-step explanation:

Given :-

a/b = (-27/64)^3 ÷ (-3/4)^5

To find :-

Find the value of (a/b)^2?

Solution :-

Given that :-

a/b = (-27/64)^3 ÷ (-3/4)^5

It can be written as

a/b =[ (-3)³/(4)³]³ ÷ (-3/4)⁵

=> a/b = [(-3/4)³]³ ÷ (-3/4)⁵

Since (a/b)^n = a^n / b^n

=> a/b = [(-3/4)^3×3]÷(-3/4)⁵

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

=> a/b = (-3/4)⁹ ÷ (-3/4)⁵

=> a/b = (-3/4)⁹ ÷ (-3/4)⁵

RHS is in the form of a^m / a^n

Where a = -3/4 ,m = 9 and n = 5

We know that

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

=> a/b = (-3/4)^(9-5)

=> a/b = (-3/4)⁴

Therefore a/b = (-3/4)⁴

On squaring both sides then

=> (a/b)² = [(-3/4)⁴]²

We know that

(a^m)^n = a^mn

=> (a/b)² = (-3/4)^(4×2)

=> (a/b)² = (-3/4)⁸

or

=> (a/b)²

= (-3×-3×-3×-3×-3×-3×-3×-3)/(4×4×4×4×4×4×4×4)

= 6561/65536

Answer:-

The value of (a/b)² for the given problem is (-3/4)⁸ or 6561/65536

Used formulae:-

• a^m / a^n = a^(m-n)

• (a^m)^n = a^mn

• (a/b)^n = a^n / b^n