Please explain the following with what happens with exponents that have a negative number and adds up to zero?

Question

1. P^0 x^-1 (x-2x^0)

Step1 p^0 x^-1(x) – p^0 x^-1 (2x^0)

Step2 x^0 - 2x^-1

Step3 1 - 2x^-1

Why does p^0 get dropped in step 2
Why does x^0 in step 2 become 1 in step three

2. Y^0 x^-4 (x^4 – 5 y^4 x^4)

Step1 x^-4 (x^4) - 5 y^4 x^4 (x^-4)

Step2 x^0 - 5 y^4 X^0

Step3 1 - 5 y^4

Why does the one lot of x become 1 and the other x just dropped

Thankyou for the help

Answer 1

I have forgotten the proof but cellphone is correct a number to the zero power becomes the value of 1. you can do that anytime in the equation, step 1 is a good choice it give less mess to work with.

for your 2nd eqn

(y^0/x^4)(x^4-5y^4x^4)

1) (1/x^4)(x^4 - 5y^4x^4)

2) x^4/x^4 - (5y^4x^4)/x^4
all the factor of x cancel
3) 1-5y^4(1)
remember in multiplication 1 is the identity any value times 1 gives you the original value

Answer 2

Question 1
ANY number to the power of zero = 1
This can be checked by using a calculator.

Thus p^(0) = 1 and x^(0) = 1

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

Question 2
when multiplying,add indices
eg x² times x³ = x^(5)

x^(- 4).[ (x^(4) - 5 y^(4).x^(4)]
= x^(0) - 5y^(4).x^(0)
= 1 - 5.y^(4)

Answer 3

a number or variable having an exponent of zero is equivalent to 1... always

and a number or a variable having an exponent of negative means you have to get the inverse of that number... for example

x^-1 is equal to 1 / x

or

x^-2 is equal to 1 / x^2

Answer 4

by definition a zero exponent reduces its base to "1". So, if you were multiplying it would disappear.

Answer 5

As a teacher, you need to...XeA