Question

Please solve the question in the attachment above
thanks in advance​

Answer 1

2
`^{-(19)/(2) }`

Explanation:

Given expression:

(√4)⁻⁷ x (√2)⁻⁵

To solve this problem, we are going to use some rules of exponent;

(√4)⁻⁷ x (√2)⁻⁵

4 = 2²

= (√2²)⁻⁷ x (√2)⁻⁵

√x² = x
`^{2x (1)/(2) }`

= ( 2
`^{2x(1)/(2) }`) ⁻⁷ x (2
`^{(1)/(2 )`)⁻⁵

= 2⁻⁷ x 2
`-(5)/(2)`

aˣ x aⁿ = aˣ⁺ⁿ

So;

2⁻⁷ x 2
`-(5)/(2)` = 2
`^{-7 + (-(5)/(2) )}`

= 2
`^{-7 - (5)/(2) }`

= 2
`^{-(19)/(2) }`