PLease Help Me With These Math Questions?

Question

1) MUltiply. Write the product in scientific notation.
(3.6 * 10^ -4)(9 * 10^8)

2) 24x^2y / 8x^3y^2

3) 3x^2 + 2x(x-1)

4) (-2)^3 / ( -2)^3

Answer 1

2. (24x^2y)/(8x^3y^2)

First: simplify the coefficients...

24/8 = 3

(3x^2y)/(x^3y^2)

Sec: simplify the x-variables --- when your dividing the same variables > subtract the exponents...

x^2/x^3
x^(2-3)
x = -1

(3x^-1y)/(y^2)

*Simplify the y-variables > subtract the exponents...

y/y^2
y^(1-2)
y^-1

(3x^-1y^-1)/1

Third: rule - variables can't have negative exponents; make them
positive by placing them in the denominator...

(3)/(xy)
P.S. you don't need to write "1" as the exponent.

3. 3x^2 + 2x(x-1)

First: eliminate parenthesis --- distribute the outer term with the terms in parenthesis...

3x^2 + 2x(x) + 2x(-1)
3x^2 + 2x^2 + (-2x)
3x^2 + 2x^2 - 2x

Sec: combine "like" terms...

5x^2 - 2x

4. (-2)^3 / ( -2)^3

First: cancel both terms because they are the same...

1/1

Sec: your left with 1/1 which is...

= 1

Answer 2

1)
(3.6 * 10^ -4)(9 * 10^8)
= (3.5 * 9) * 10^(8 - 4)
= 31.5 * 10^4

2)
24x^2y / 8x^3y^2
= (24/3) x^(2-3) y^(1-2)
= 8 / xy

3)
3x^2 + 2x(x-1)
= 3x^2 + 2x^2 - 2x
= 5x^2 - 2x
= x(5x - 2)

4)
(-2)^3 / ( -2)^3
= (-2)^(3 - 3)
= (-2)^0
= 1