Question

Drag expressions to complete each equation.

Answer 1

`a^(-b) =(1)/(a^(b))`

`(a^(b))/(a^(c)) = a^(b-c)`

`(a^(c))/(b^(c)) =((a)/(b) )^(c)`

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

For example:

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

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

When you have an exponent divided by an exponent, you subtract the exponents together.

For example:

`(x^5)/(x^2) =x^(5-2) =x^3`

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

When you multiply an exponent directly into a variable with an exponent, you multiply the exponents together.

For example:

`(x^(2) )^(4) = x^8`

`((x^2)/(y^3) )^5=(x^(10))/(y^(15))`

`((x^1)/(y^1) )^b = (x^b)/(y^b)`