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

1 Answer

16^-2

Explanation:

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