Question

How do you simplify `\frac { 6^ { - 7} ( 6^ { - 2} ) } { 6^ { 10} }`?

Answer 1

`1/(6^19)`

Explanation:

Usually when it says simplify with negative exponents we want to write the expression with positive exponents.

Looking at the expression in the numerator:

`6^-7(6^-2)` we can use the product rule where if you have two powers with the same base you simply add the exponents

So,
`6^-7(6^-2)=6^(-7+(-2))=6^-9`

Now, looking at the entire expression, we have `6^-9-:6^10` so we can use the quotient rule where if you have two powers with the same base you simply subtract the exponents

So,
`6^-9-:6^10=6^(-9-10)=6^-19`

Finally we want to make it so we have positive exponents. Using the fact that `b^-x=1/(b^x)`

We get `6^-19=1/(6^19)`