third fourth and fifth index law

taeyongtaehyung

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May 21, 2021
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do we use third fourth and fifth index law in one algebra expression

Simplify the following, using the third, fourth and fifth index laws.
a) (b^2)^4
b) (2m^2)^3
 
I have never seen them numbered before but the "index laws" that appear to be relevant here are
(xn)m=xmn\displaystyle (x^n)^m= x^{mn} and (xy)n=xnyn\displaystyle (xy)^n= x^ny^n.

Using the second of those, (2m2)3=23(m2)3=8m6\displaystyle (2m^2)^3= 2^3(m^2)^3= 8m^6.
 
I always say to my students: "If in doubt, expand it out!"

(2m2)3=2m22m22m2=2mm2mm2mm=8m6\displaystyle (2m^2)^3 = 2m^2 * 2m^2 * 2m^2 = 2*m*m * 2*m*m * 2*m*m = 8m^6
 
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