Exponents

[asissa]

Is this correct? If not, can you please show me where the mistake is? I'm working on this with my kids, and we are getting different answers. Thanks!

 

[mmm4444bot]

Your reasoning is good, and your end-result is correct.

(I ignored the Rational number 30/8, that appears in front of result #3.)

I see only one error; it happened when going from result #1 to result #2.

(-3)^(-3) = -1/27, not 1/27.

You recovered from this sign error, in the next step, because (-27)^2 is 729.

Good job ~ Mark

PS: There are several other ways, to simplify the given expression.

 

[Denis]

You can reduce the work quite a bit this way; switch numerator and denominator:

(2 x^4 y^-8)^2 / (-3 x^2 y^5)^3

= (4 x^8 y^-16) / (-27 x^6 y^15)

= (4 x^2) / (-27 y^31)

Now square above:
(16 x^4) / (729 y^62)