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

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

Answer
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.

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