Simplify the Expression: (2x^n/y^n)*(y/2x)^2
Answer STEP 1:
Observe the given expression:
If you observe the expression, then you notice that it contains a term in which a quotient is raised to a power. The first step in simplifying the expression will obviously be to simplify that term.
The exponent law which can be helpful for this purpose is:
The law simply means to bring the power into each term of the quotient. See what happens when we apply this law.STEP 2:
The simplification of the term isn’t over yet. The denominator (2x)2
can be rewritten using the law
: (ab)n = anbn
Keep in mind that to raise a term to the second power means to multiply it by itself two times.STEP 3:
What we want to do here is to write as a product of quotients such that all expressions with like bases are brought together.
Since 4 goes evenly into 2, you cancel these numbers.STEP 4:
Now, the operation left is to divide powers with like bases
. When you divide, the exponents subtract.
The final simplified expression that you get is: