How do you simplify #8^ {1 2} \cdot ( 8^ { 7} ) ^ { - 2}#?

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Answer 1 · 2017-09-16T02:08:23

Expression #=1/64#

Expression #= 8^12xx(8^7)^(-2)#

Here we will apply three of the laws of indices as follows:

(i) #(a^m)^n = a^(mxxn)#

(ii) #a^m xx a^n = a^(m+n)#

(iii) #a^-n = 1/a^n#

Apply (i) to the second term of the product:

Expression #= 8^12xx8^((7xx-2)) = 8^12xx8^(-14)#

Apply (ii)

Expression #=8^((12-14)) = 8^-2#

Apply (iii)

Expression #=1/8^2 = 1/64#