Question

Simply the expression. write your answers using only positive exponents.

Answer 1

We can apply the exponent rules to solve this problems.

2) In this case we have to convert the negative exponent into a positive exponent. We can do it like this:

`y^(-5)=(1)/(y^5)`

3) In this case we applied the same rule as in (2) for the y exponent:

`9x^6y^(-3)=9x^6\cdot(1)/(y^3)=(9x^6)/(y^3)`

4) In this case, we can simplify the expression as:

`(5^6)/(5)=(5^6)/(5^1)=5^6\cdot5^(-1)=5^(6-1)=5^5=3125`

5) We apply the product rule:

`4^(-3)\cdot4^5=4^(-3+5)=4^2=16`

6) We apply the power rule:

`(w^5)^7=w^(5\cdot7)=w^(35)`

7) We can simplify this as:

`(-5z)^3=(-5)^3\cdot z^3=-125z^3`