- TheEdwardsFamily

PLEASE HELP ME!!!!!!!! I'LL MEDAL!
What is the missing exponent?
(10^6) ____ = 10 ^-18

- schrodinger

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- TheEdwardsFamily

- anonymous

Are you familiar with logs?

- TheEdwardsFamily

no...

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## More answers

- anonymous

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

- TheEdwardsFamily

yes

- anonymous

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

- TheEdwardsFamily

im trying to find the missing exponent

- anonymous

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\[\left( 10^6 \right)^x\]

- TheEdwardsFamily

10^6 is 60

- anonymous

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

- anonymous

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

- TheEdwardsFamily

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

- anonymous

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

- TheEdwardsFamily

6?

- anonymous

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

- TheEdwardsFamily

8th grade

- anonymous

Have you done algebra?

- TheEdwardsFamily

yes

- anonymous

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

- TheEdwardsFamily

yes. i have.

- anonymous

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)

- TheEdwardsFamily

multiplication

- anonymous

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

- TheEdwardsFamily

yes

- anonymous

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

- TheEdwardsFamily

mmm....im thinking 3

- anonymous

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?

- TheEdwardsFamily

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

- TheEdwardsFamily

I was just confused at the beginning

- anonymous

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

- anonymous

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?

- anonymous

Sorry. Gotta run. Good luck finishing it off.

- TheEdwardsFamily

ok thanks for your help!

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