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5 votes
Would (6^3)^-3 cancel out to just 6? Or it will be 6^0?

2 Answers

6 votes

(a^b)^c=a^(bc) so

(6^3)^(-3)=6^((3)(-3))=6^(-9) =
(1)/(6^9)

User AnnanFay
by
7.7k points
7 votes
The rule for an exponent raised to another exponent is:

(a^b)^c is equal to a^(b*c) so in this case:

(6^3)^(-3) is equal to:

6^(-9) which is

1/(6^9) which is:

1/10077696

What you described is what happens when you multiply two similar bases with exponents, for example

(a^b)(a^c)=a^(b+c) so if your problem was:

(6^3)(6^-3) then yes it would be equal to:

6^(3-3)

6^0

1

So keep those rules in mind...

(a^b)(a^c)=a^(b+c)

and

(a^b)^c=a^(b*c)


User Finn Bear
by
7.5k points

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