(1/9e^6x)^-1/2. how do i do this?
To simplify the expression (1/9e^6x)^(-1/2), we can follow these steps:
Step 1: Start by understanding the reciprocal property of exponents.
- The reciprocal property of exponents states that a^(m/n) is the same as taking the nth root of a raised to the power of m. In other words, a^(m/n) = ∛(a^m) if n = 3, and so on.
Step 2: Apply the reciprocal property of exponents to transform the expression.
- Applying the reciprocal property to our given expression, we can rewrite it as [(1/9e^6x)^(1/2)]^(-1).
- Since the exponent is now positive, we can remove the parentheses and rewrite the expression as (1/9e^6x)^(1/2).
Step 3: Simplify the expression further.
- To simplify (1/9e^6x)^(1/2), we can simply take the square root of 1/9e^6x.
- The square root of a fraction is the same as taking the square root of the numerator and the square root of the denominator.
Therefore, the simplified expression is (√1)/(√9e^6x), which can be further simplified to 1/(3e^3x).