Question

please refer to the below attachment​

Answer 1

Step-by-step explanation:

Given:-

√[(1/4)+(0.01)^(-1/2)-(27)^(2/3)]

To find:-

Find the solution for the given problem

Solution:-

Given that

√[(1/4)+(0.01)^(-1/2)-(27)^(2/3)]

=>√[(1/4)+(1/100)^(-1/2)-(3^3)^(2/3)]

=>√[(1/4)+{(1/10)^2}^(-1/2)-(3^3)^(2/3)]

We know that (a^m)^n = a^(m+n)

=>√[(1/4)+{(1/10)^2}^(-1/2)-(3)^(2×3/3)]

=>√(1/4)+{(1/10)^2}^(-1/2)-3^2]

We know that a^-n = 1/a^n

=>√[(1/4)+{(1/10)^2}^(-1/2)-3^2]

=>√[(1/4)+(10^(-2×-1/2)-9]

=>√[(1/4)+(10^1)-9]

=>√[(1/4)+10-9]

=>√[(1/4)+1]

=>√[(4+1)/1]

=>√(5/4)

=>(√5)/2

Answer:-

The solution for the given problem is

√5 /2

Used formulae:-

• a^-n = 1/a^n
• (a^m)^n = a^mn