third fourth and fifth index law

[taeyongtaehyung]

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

 

[Deleted member 4993]

do we use third fourth and fifth index law in one algebra expression

Can you please describe those laws - according to your text book or your class-notes?

 

[HallsofIvy]

I have never seen them numbered before but the "index laws" that appear to be relevant here are
\(\displaystyle (x^n)^m= x^{mn}\) and \(\displaystyle (xy)^n= x^ny^n\).

Using the second of those, \(\displaystyle (2m^2)^3= 2^3(m^2)^3= 8m^6\).

 

[Harry_the_cat]

I always say to my students: "If in doubt, expand it out!"

\(\displaystyle (2m^2)^3 = 2m^2 * 2m^2 * 2m^2 = 2*m*m * 2*m*m * 2*m*m = 8m^6\)