How do you simplify #(c^3)^4#?

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Answer 1 · 2016-10-02T21:51:30

#c^12#

While there is a law of indices which we could use, let's use basics.

#x^4 " means " x xx x xx x xx x#

In the same way #(c^3)^4 " means " c^3 xx c^3 xx c^3 xx c^3#

The bases are all the same, so add the indices to get #c^12#

A quicker method is using the power law :#(x^m)^n = x^(mxxn)#

"raising a power to another power, times the indices"

#(c^3)^4 = c^(3xx4) = c^12#