Under root 4 raised power minus 3 by 4
(2)minus power3/4. (1/2) power3/4 ( (1/2) power3 ) hole power1/4
To simplify the expression √4^(-3/4), we can follow these steps:
Step 1: Evaluate the exponent.
4^(-3/4) = 1 / (4^(3/4))
Step 2: Simplify the expression inside the parentheses.
4^(3/4) = (2^2)^(3/4) = 2^(2*(3/4)) = 2^(3/2)
Step 3: Rewrite the expression.
√4^(-3/4) = √(1 / (2^(3/2)))
Step 4: Simplify the square root.
√(1 / 2^(3/2)) = 1 / √(2^(3/2))
Step 5: Simplify the expression under the square root.
√(2^(3/2)) = √(2 * (2^(1/2))) = √(2) * √(2^(1/2)) = √(2) * 2^(1/4)
So, the final simplified expression is:
√4^(-3/4) = 1 / (√(2) * 2^(1/4))
To solve this expression, we need to break it down step by step.
The expression we have is √(4^(-3/4)).
Step 1: Simplify the exponent
In this case, we have a negative exponent. To simplify, we can apply the rule that a^(-n) = 1/(a^n).
So, 4^(-3/4) = 1/(4^(3/4)).
Step 2: Simplify the root
The square root (√) of a number can also be written as a fractional exponent. So, √a = a^(1/2).
In our case, √(4^(-3/4)) can be written as (4^(-3/4))^(1/2).
Step 3: Apply exponent properties
To simplify, we can combine these two exponents:
(4^(-3/4))^(1/2) = 4^((-3/4)*(1/2)).
Multiply the exponents:
4^((-3/4)*(1/2)) = 4^(-3/8).
Step 4: Simplify the resulting exponent
To evaluate 4^(-3/8), we can use the exponent rule that (a^m)^n = a^(m*n).
So, 4^(-3/8) = (4^(-3/8))(1).
Step 5: Evaluate the expression
Now, we have 4^(-3/8) as the final expression. To evaluate this, you can use a calculator or convert it to a radical form.
If you evaluate it using a calculator, you will get the decimal value of the expression.
If you want to convert it to radical form, you can use the rule that a^(m/n) = n√(a^m).
So, 4^(-3/8) as a radical would be expressed as the 8th root of 4^(-3).
To summarize:
√(4^(-3/4)) = 4^(-3/8)
You can calculate 4^(-3/8) using a calculator or express it as the 8th root of 4^(-3).
if you mean this
sqrt(4-3/4) then
remember 4 cubed is 64, the fourth root of 64 is 2sqrt2
then answer=1/2sqrt2 or sqrt2/4