Question

please tell me the answer please fast​

Answer 1

Step-by-step explanation:

Given :-

(3^-3×16^5/4 ÷ 729^-1/3)^-1/2

To find :-

Find the value of the expression ?

Solution :-

Given expression is (3^-3×16^5/4 ÷ 729^-1/3)^-1/2

It can be written as

=> [ 3^-3 × (2^4)^(5/4) ÷ (3^6)^(-1/3)]^(-1/2)

We know that

(a^m)^n = a^mn

=>[ 3^-3 × 2^(4×5/4) ÷ 3^(6×-1/3)]^(-1/2)

=> [( 3^-3)×(2^5)÷(3^-2)]^(-1/2)

=> [(3^-3)×(2^5)/(3^-2)]^(-1/2)

=> [(3^-3)×(2^5)/(3^-2)]^(-1/2)

We know that

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

=>[ {3^(-3-(-2))}×(2^5)]^(-1/2)

=> [ {3^(-3+2)}×(2^5)]^(-1/2)

=> [ (3^-1)×(2^5)]^(-1/2)

We know that

a^-n = 1/a^n

=>[ (2^5)/3 ]^(-1/2)

=> (3/2^5)^2

=>3²/(2^5)^2

=> 3²/2¹⁰

=> 9/1024

Answer:-

The value of the given expression is 9/1024

Used formulae:-

• (a^m)^n = a^mn

• a^-n = 1/a^n

• a^m/a^n = a^(m-n)

• (a^m× a^n = a^(m+n)

• (a/b)^m = a^m / b^m