How do you simplify (4×10−5)−6 ?

(4⋅10−5)−6

Does the raising a power to an exponent rule apply here when you multiply -5 by -6?

Thanks.

2 Answers
Jumbotron
Apr 8, 2018

Yes it does affects the exponent, for example;

Explanation:

(a2)3=(a2)(a2)(a2)=(a2+2+2)=a6

Same thing as;

(a2)3=(a2×3)=a6

Also recall;

a−2=1a2

Now we solve the question;

(4×10−5)−6=(4−6×10−5×−6)=4−6×1030

or

(4×10−5)−6=1(4×10−5)6=146×10−5×6=146×10−30=(46×10−30)−1=(46×−1×10−30×−1)=4−6×1030

EZ as pi
Apr 9, 2018

146×10−30=103046

Explanation:

The rule of multiplying the indices does apply here.

However, notice that there are twp factors inside the bracket so both of them have to be raised to the power of −6

(4×10−5)−6 → compare with (xy2)5=x5y10

=4−6×10−5×−6

=4−6×1030

=103046

You could also answer as 1(4×10−5)6

Which leads to 146×10−30

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