# scientific notation world problem and 2 polynomial questions

#### ayva00

##### New member
These are some homework problems i have that i'm a bit confused about.

simplify: 2(-50)^0-2^-3 so i did 2(1)-2^-3 then 2+8= 10, did i do that problem correctly?

write the coefficient of the third degree term of the polynomial in the blank: 5x^4-8x^3-6x+16, does the 3rd degree mean the 3rd polynomial or the polynomial with the exponent of 3. I'm thinking it's the the first option, so the answer would be -6.

and lastly this word problem,
Write the numbers one million and one millionth in scientific notation. By what number must we multiply one millionth to get one million?
So i wrote 1,000,000 and 1 x 10^6. So is the answer 6? or just 1 maybe? :/

Thanks so much, i really appreciate the help.

#### fasteddie65

##### Full Member
"simplify: 2(-50)^0-2^-3 so i did 2(1)-2^-3 then 2+8= 10, did i do that problem correctly?"
No. 2^(-3) = 1/8 2 - 1/8 = 15/8

"write the coefficient of the third degree term of the polynomial in the blank: 5x^4-8x^3-6x+16, does the 3rd degree mean the 3rd polynomial or the polynomial with the exponent of 3. I'm thinking it's the the first option, so the answer would be -6."
The 3rd degree term is the term with a 3 exponent on the variable, so the answer is -8.

"and lastly this word problem,
Write the numbers one million and one millionth in scientific notation. By what number must we multiply one millionth to get one million?
So i wrote 1,000,000 and 1 x 10^6. So is the answer 6? or just 1 maybe? :/"
You write the numbers correctly. The number by which you multiply one millionth by to get one million is 1 • 10^12.

#### ayva00

##### New member
The last two i understand, but the first one, i'm a little lost how you got the fraction. -2^-3 isnt going to be 8? or -8 even?
Sorry, i'm just trying to understand. Thanks for your help

#### Denis

##### Senior Member
RULE: a^(-p) = 1 / a^p ; so 2^(-3) = 1 / 2^3

#### ayva00

##### New member
Denis said:
RULE: a^(-p) = 1 / a^p ; so 2^(-3) = 1 / 2^3
I notice that you're not including the negative infront of the 2, is there a reason for that or are you just not writing it?
thanks

#### Denis

##### Senior Member
That "negative" has nothing to do with the value of 2^(-3).
It simply means to subtract that value.

#### Subhotosh Khan

##### Super Moderator
Staff member
Remember:

$$\displaystyle (-a)^n$$

is usually different from

$$\displaystyle -(a)^n$$

#### ayva00

##### New member
Ohhh okay, i got it. Thanks so much