Simplify the Expression (2a^6/b^7)(-b^4/a^2)^3

Simplify the expression (2a^6/b^7)(-b^4/a^2)^3

STEP 1:   Observe the given expression:

simplify this algebraic equation
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 law (a/b)^n = a^n/b^n
The law simply means to bring the power into each term of the quotient. See what happens when we apply the law.

applying the exponent law
STEP 2:    The numerator and the denominator of that fraction still contain powers raised to the third power. Multiply the exponents making use of the law:
                                        (am)n = amn

We get:

applying another exponent law
STEP 3:     What we want to do here is to write as a product such that all expressions with like bases are brought together.

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

The final simplified expression that you get is –2b5.

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
Graphs & Equations
Useful Resources