simplify by removing radical signs and negative indices where ever they occur:-
¡Ì4 power -3/4
I can not fathom your notation.
To simplify the expression √(4^(-3/4)), let's start by understanding the meaning of a negative exponent.
A negative exponent indicates that the base should be inverted, or put into the denominator. The exponent's absolute value tells us what power the base should be raised to. In this case, we have 4^(-3/4). The negative exponent (-3/4) means we should invert the base 4 and raise it to the power of 3/4.
Now, let's simplify the expression step by step:
1. Invert the base: 4^(-3/4) becomes 1/4^(3/4).
2. Remove the negative exponent by taking the reciprocal: 1/4^(3/4) becomes 1/(4^(3/4)).
3. To simplify the expression further, let's rewrite 4^(3/4) using a radical. The exponent 3/4 represents the fourth root of 4 raised to the power of 3: ∛(4^3).
4. Simplify the exponent: 4^3 equals 64, so we have ∛64.
5. Calculate the cube root of 64, which equals 4: ∛64 = 4.
So, the simplified expression is 1/4^(3/4) = 1/∛64 = 1/4.