A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

What is the missing value? 3^-6/3^?=3^4 A. −10 B. −2 C. 2 D. 10

  • This Question is Closed
  1. whpalmer4
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\frac{3^{-6}}{3^?} = 3^4\] Remember that \[\frac{a^m}{a^n} = a^{m-n}\]

  2. whpalmer4
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So that means \[\frac{3^{-6}}{3^?} = 3^{-6-?} = 3^4\]or \[-6-?=4\]Can you solve for ?

  3. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ???

  4. whpalmer4
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The exponent needs to be a number such that -6 -<some number> = 4. Maybe you're confused because I didn't use a typical variable name, like \(x\). \[-6-x = 4\] Can you solve that for \(x\)? \(x\) is the exponent for the number in the denominator in the problem.

  5. whpalmer4
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Or, you could solve it a different way: \[\frac{3^{-6}}{3^x} = 3^4\]Let's multiply both sides by \(3^x\): \[3^x*\frac{3^{-6}}{3^x} = 3^4*3^x\]\[\cancel{3^x*}\frac{3^{-6}}{\cancel{3^x}} = 3^4*3^x\]\[3^{-6} = 3^4*3^x\] Now when we multiply exponentials with the same base, as we have here (everything is 3 to some power, 3 is the base), we keep the base and ADD the exponents. \[3^2*3^3 = 3^{2+3} = 3^5\]just like if we did it the long way:\[3^2*3^3=(3*3)*(3*3*3) = 3*3*3*3*3=3^5\] so \[3^{-6}=3^4*3^x \]\[3^{-6} = 3^{4+x}\]and the only way that can be true is if \[-6 = 4+x\] Solve for \(x\) and you have your answer.

  6. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.