How do you simplify #(343 u^4 c^-5) /(7 u^6 c^-3)^-5#?

3 Answers
CrispyRounds · EZ as pi
Aug 8, 2018

#(5764801u^34)/(c^20)#

Explanation:

There is a negative exponent rule, I'm not quite sure if it has a name, but it says that a negative exponent in the numerator can be moved to the denominator and become positive, and vice versa.
An example would be #x^-2=1/x^2#

So using this

#((7u^6c^-3)^5(343u^4))/c^5#

Then we can distribute the exponent, #5#, in the numerator
#(16807u^30c^-15(343u^4))/c^5#

Now we can move the #c^-15# to the denominator using the negative exponent rule
#(16807u^30(343u^4))/(c^5*c^15)#

We can now combine like bases

#(5764801u^34)/(c^20)#

Mark D.
Aug 9, 2018

#(x^a)^b=x^(axxb)#

#[343u^4c^-5]/(7u^6c^-3)^-5=[7^3u^4c^-5]/(7^-5u^-30c^15)#

#x^a/x^b=x^(a-b)#

#7^8u^34c^-20#

or #[7^8u^34]/c^20#

EZ as pi
Aug 9, 2018

#(7^8u^34)/(c^20)#

Explanation:

#(343u^4c^-5)/(7u^6c^-3)^-5#

Use the law of indices for negative indices:

#x^-m = 1/x^m#

#=(343u^4xx(7u^6c^-3)^5)/c^5#

Note that #343 = 7^3#

It is better to keep the numbers in index form.

#=(7^3u^4 xx 7^5u^30c^-15)/c^5#

#=(7^3u^4 xx 7^5u^30)/(c^5 xxc^15)#

Add the indices of like bases:

#=(7^8u^34)/(c^20)#

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