Question

How do you simplify `\frac { a ^ { 7} \cdot a ^ { 6} } { a ^ { - 6} }`?

Answer 1

`a^19`

Explanation:

We know `a^-1 = 1/a. Then 1/a^-1 = a^1`

Hence `[a^7. a^6]/a^-6 = a^7. a^6. a^6`

`rArr a^[7+6+6] = a^19` [as the base are same]

Answer 2

See the entire simplification process below:

Explanation:

First, combine the terms in the numerator using this rule of exponents:

`x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))`

`(a^color(red)(7) * a^color(blue)(6))/a^-6 = a^(color(red)(7) + color(blue)(6))/a^-6 = a^13/a^-6`

Now, use this rule of exponents to combine the numerator and denominator:

`x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))`

`a^color(red)(13)/a^color(blue)(-6) = a^(color(red)(13)-color(blue)(-6)) = a^(color(red)(13)+color(blue)(6)) = a^19`