Question

PLEASE HELP ME!!!!!!!! I'LL MEDAL!

What is the missing exponent?

(10^6) ____ = 10 ^-18

Answer 1

@Nnesha

Answer 2

Are you familiar with logs?

Answer 3

no...

Answer 4

I'm having trouble with the question. Is it\[(10^6)^x = 10^{-18}\]

Answer 5

yes

Answer 6

10 to the power 6 = 1,000,000 start there

Answer 7

im trying to find the missing exponent

Answer 8

OK. Then no logs required. This question involves using the laws of exponents. The law you need to understand to answer this question is the "power to a power" law. It say that when you have a power raised to another power, you multiply the exponents together. IN other words\[\left( b^n \right)^m = b^{nm}\] So, what is\[\left( 10^6 \right)^x\]

Answer 9

10^6 is 60

Answer 10

No. Leave the base (10) alone and just multiply the two exponents. What is \(6 \times x\) ?

Answer 11

\[\left( 10^6 \right)^x = 10^{6 \times x} = ?\]

Answer 12

so i am multiplying 6 * 6? im confused. (math is not my favorite subject.)

Answer 13

No. Multiply 6 times x. What do you get?

Answer 14

6?

Answer 15

May I ask what course this is for? What grade level?

Answer 16

8th grade

Answer 17

Have you done algebra?

Answer 18

yes

Answer 19

So have you solved problems like\[3x=18\]/etc.

Answer 20

yes. i have.

Answer 21

OK. Good. So when you see \(3x\) as above, what mathematical operation is going on between the 3 and the x? (Addition, subtraction, multiplication, division)

Answer 22

multiplication

Answer 23

Excellent. So\[3 \times x = 3x\]right?

Answer 24

yes

Answer 25

OK. Back to your question. What is \(6 \times x\) ?

Answer 26

mmm....im thinking 3

Answer 27

I'm sorry, I'm trying to determine where you're confused. You were just able to determine that\[3 \times x = 3x\] but you're having difficulty with\[6 \times x = ?\]Can you tell me what's confusing you?

Answer 28

ok, i think i understand now 6 * x =6x

Answer 29

I was just confused at the beginning

Answer 30

Yes! So, we've got your problem down to this:\[\left( 10^6 \right)^x = 10^{-18}\]\[10^{6 \times x} = 10^{-18}\]\[10^{6x} = 10^{-18}\]

Answer 31

Now at this point, we have a single power on each side of the equation and these powers have the same base, i.e. 10. So now you can forget the bases and equate just the exponents, i.e.\[6x = -18\]Can you solve this for x?

Answer 32

Sorry. Gotta run. Good luck finishing it off.

Answer 33

ok thanks for your help!