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Simplify #(a^3b^2)^-2 xx (a^2b^3)^4# ?

Answer 1

Ethan Adkins

#a^2b^8#

Apply two of the rules of indices:

#(a^n)^m = a^(nxxm)# (1)

#a^nxxa^m = a^(nxxm)# (2)

Here our expression is: #(a^3b^2)^-2 xx (a^2b^3)^4#

Apply (1) to both terms: #-> a^(-6)b^(-4) xx a^8b^12#

Group powers of #a# & #b# and apply (2) #-> a^((-6+8))xxb^((-4+12))#

#= a^2xxb^8 = a^2b^8#

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Answer 2

Nathan Axel

The simplified expression is ( \frac{b^{16}}{a^{10}} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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