Question

Which expression is equivalent to 7^3⋅ 7^-5 as a fraction

Answer 1

When you multiply a base with an exponent by a base with an exponent, you add the exponents together. (But you can only combine the exponents when the bases are the same)

For example:

`x^3(x^1)=x^((3+1))=x^4` (they have the same base of x)

`y^3(x^2)=y^3x^2` (you can't combine the exponents because they have different bases of y and x)

`2^2(2^1)=2^((2+1))=2^3=8`

When you have a negative exponent, you move the base with the negative exponent to the other side of the fraction to make the exponent positive.

For example:

`x^(-3)` or
`(x^(-3))/(1) =(1)/(x^3)`

`(1)/(y^(-2)) =(y^2)/(1)` or
`y^(2)`

`7^3*7^(-5)` Add the exponents together

`7^((3+(-5)))`

`7^(-2)` Make the exponent positive

`(1)/(7^2)` Simplify

`(1)/(49)`