Question
upstudy study bank question image url

d. \( \left(\frac{3^{7}}{3^{5}}\right)^{-2} \)

Ask by Ryan Donnelly. in Colombia
Mar 15,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

La respuesta es \( \frac{1}{81} \).

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

Extra Insights

Let's break it down! First, you can simplify the expression inside the parentheses: \( \frac{3^{7}}{3^{5}} \) equals \( 3^{7-5} = 3^{2} \). Now, you have \( (3^{2})^{-2} \). Using the power of a power property, you multiply the exponents: \( 3^{2 \cdot -2} = 3^{-4} \). This can be rewritten as \( \frac{1}{3^{4}} \), which is \( \frac{1}{81} \). So, the final answer is \( \frac{1}{81} \). It's like unwrapping layers of a gift - you simplify step-by-step to reach the exciting conclusion!

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy