Simplify the Expression: (2x^n/y^n)*(y/2x)^2

Question
Simplify (2x^n/y^n)*(y/2x)^2
Answer
STEP 1:   Observe the given expression:


simplify this 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:

exponent rule

The law simply means to bring the power into each term of the quotient. See what happens when we apply this law.

using the exponent rule

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.

using another exponent rule
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.

using the exponent rule

Since 4 goes evenly into 2, you cancel these numbers.

simplifying further

STEP 4:    Now, the operation left is to divide powers with like bases. When you divide, the exponents subtract.

final answer

The final simplified expression that you get is:

simplify this algebraic fraction

Click here to post comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Exponents Library.

iPod Touch & iPhone
iPad
Graphs & Equations
Algebra
Exponents
Symmetry
Fractions
Measurements
Interest
Angles
Triangles
Useful Resources