To simplify the expressions given:
C = (4^2√3 - 4^√3 - 1)*2^(-2√3)
= (16√3 - 4√3 - 1)*(1/(2^2√3))
= 12√3 - 1 * (1/(2^2√3))
= (12√3 - 1) / 2^(2√3)
Now, let's simplify D:
D = (10^2 + √7) / (2^2 + √7*5 + √7)
= (100 + √7) / (4 + 5√7 + √7)
= (100 + √7) / (4 + 6√7)
= (100 + √7) / 4(1 + 1.5√7)
= (100 + √7) / 4(1.5√7)
= (100 + √7) / 6√7
= (100√7 + 7) / 6√7
Therefore, C = (12√3 - 1) / 2^(2√3) and D = (100√7 + 7) / 6√7.
To simplify the expressions given:
C = (4^2√3 - 4^√3 - 1)*2^(-2√3)
= (16√3 - 4√3 - 1)*(1/(2^2√3))
= 12√3 - 1 * (1/(2^2√3))
= (12√3 - 1) / 2^(2√3)
Now, let's simplify D:
D = (10^2 + √7) / (2^2 + √7*5 + √7)
= (100 + √7) / (4 + 5√7 + √7)
= (100 + √7) / (4 + 6√7)
= (100 + √7) / 4(1 + 1.5√7)
= (100 + √7) / 4(1.5√7)
= (100 + √7) / 6√7
= (100 + √7) / 6√7
= (100√7 + 7) / 6√7
Therefore, C = (12√3 - 1) / 2^(2√3) and D = (100√7 + 7) / 6√7.