Question

Simplify each expression. Use positive exponents.

1. m3n-6p0

2. a^4b^-3/ab^-2

3. (x^-2y^-4x^3) -2

Answer 1

Explanation:

(A) The given expression is:

`m^3n^(-6)p^0`

Simplifying this expression, we get

=
`m^3n^(-6)(1)`

=
`(m^3)/(n^6)`

which is the required simplified form.

(B) The given expression is:

`(a^4b^(-3))/(ab^(-2) )`

Simplifying the above equation using the exponent rule, we have

=
`(a^3)/(b)`

which is the required simplified form.

(C) The given expression is:

`(x^(-2)y^(-4)x^3)^(-2)`

Simplifying this expression, we get

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

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

=
`(y^8)/(x^2)`

which is the required simplified form.

Answer 2

To simplify each expression, we need to group all the terms that have the same bases and flock them if necessary to one side. One rule that applies is that negative exponents goes to the other side in order to be positive.

1. m3n-6p0 ; p0 =1 , so, m3/n6
2. a^4b^-3/ab^-2 = a^4a-1 / b^-2b^3 = a^3/b
3. (x^-2y^-4x^3) -2 = (x^-2x^3 y^-4 )^-2 = (x/y^4)^-2 = y^16/x^2