Question

Write a problem that simplifies to x^2 that utilizes the following exponent properties:1 Negative exponent2 Division of powers3 Power to a power

Answer 1

Lets solve the following example

`(15x^4y^(-9))/(15x^2(y^(-3))^3)`

We can note that y is raised to the negative power of -9. Then, by the inverse law of exponents, we have

`(15x^4y^(-9))/(15x^2(y^(-3))^3)=(15x^4)/(15x^2(y^(-3))^3\cdot y^9)`

because

`y^(-9)=(1)/(y^9)`

Now, we can see that

`(x^4)/(x^2)=x^(4-2)=x^2`

where we used the division rule of exponents, then our last result can be written as

`(15x^4y^(-9))/(15x^2(y^(-3))^3)=(15x^2)/(15(y^(-3))^3\cdot y^9)`

Now, by the power to a power rule, we can see that

`(y^(-3))^3=y^((-3)\cdot3)=y^(-9)`

then, our last result can be written as

`(15x^2)/(15y^(-9)\cdot y^9)`

But

`y^(-9)\cdot y^9=y^(-9+9)=y^0=1`

Then, the last result can be written as

`(15x^2)/(15(1))=(15x^2)/(15)`

Finally, since 15 divided by 15 is one, we get

`(15x^2)/(15)=x^2`

Therefore,

`(15x^4y^(-9))/(15x^2(y^(-3))^3)=x^2`

and we used the 3 properties.