How do you simplify #\frac { 16^ { 4} } { 16^ { 6} }#?

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Answer 1 · 2017-04-09T21:53:50

#16^-2#

Divide out common factors

# 16^4 /16^6 = ( 16 xx 16 xx 16 xx 16) / (16 xx 16 xx 16 xx 16 xx 16 xx 16)#

Four of the 16 divide out leaving

# 1/ (16 xx 16)# This can be written two ways

# 1/16^2# or #16^-2 #

Using the rule of exponents, we have

#16^(4-6)=16^-2#

How???

When multiplying and the bases are the same, you add the exponents.

#x^5*x^3=x^(5+3)=x^8#

When dividing and the bases are the same, you subtract the exponents.

#x^5/x^3=x^(5-3)=x^2#

Both methods give the same answer so choose whichever is easier for you to do