what is the answer to this question? I just want to double check my answer that I wrote on a test?
(3a)^1/2 x (3a)^-1/2
What was your answer?
when you multiply, you add exponents.
For example, 2^3 x 2^4 = 2^(3+4) = 2^7
Recall that negative exponents are the reciprocals of positive exponents.
2^-3 = 1/2^3 = 1/8
SO, you have
(3a)^1/2 * (3a)^-1/2
= (3a)^1/2 / (3a)^1/2 = 1
or, by adding exponents,
(3a)^1/2 * (3a)^-1/2 = (3a)^0 = 1
anything to the zeroth power is 1.
2^3/2^3 = 8/8 = 1
so, 2^(3-3) = 2^0 = 1
9a^-1/4
(3a)^2 = 9a^2
((3a)^1/2)^-1/2 = (3a)^-1/4
There's just no valid way to come up with what you got.
To find the answer to the expression (3a)^(1/2) x (3a)^(-1/2), we need to understand the properties of exponents.
The product of two terms with the same base raised to different exponents can be simplified by adding the exponents. In this case, the base is 3a, and the exponents are 1/2 and -1/2, respectively.
First, let's simplify the exponents individually.
To simplify (3a)^(1/2), we take the square root of 3a. The square root of any number x can be written as x^(1/2). Applying this, we have:
(3a)^(1/2) = √(3a)
And to simplify (3a)^(-1/2), we take the reciprocal of the square root of 3a. The reciprocal of x^(1/2) is 1/x^(1/2). Therefore:
(3a)^(-1/2) = 1/√(3a) = 1/(√3 * √a)
Now that we have simplified the exponents, we can multiply the terms together:
(3a)^(1/2) x (3a)^(-1/2) = (√(3a)) * (1/(√3 * √a))
To simplify further, we can multiply the numerators and denominators together:
(√(3a)) * (1/(√3 * √a)) = √(3a) / (√3 * √a)
Since both the numerator and denominator have square roots, we can simplify by canceling out the common factors:
√(3a) / (√3 * √a) = √(3a) / ( √3 * √a) = 1 / √3
Therefore, the final answer to the expression (3a)^(1/2) x (3a)^(-1/2) is 1 / √3.