Question
upstudy study bank question image url

Exercise 2.5 1. Simplify without using a calculator. \( \begin{array}{ll}\text { a) } \frac{20^{3} \times 25^{2} \times 4}{10^{7}} & \text { b) } \frac{10^{3} \cdot 15^{4} \cdot 6^{2}}{20^{4} \cdot 12.45^{2}} \\ \text { c) } \frac{2 \times 2^{2 a} \times 16^{2}}{4^{a+5}} & \text { d) } \frac{3^{2} \times 3^{n-1} \times 3^{0}}{9^{n-1}} \\ \text { e) } \frac{2^{m+n}}{2^{n}} & \text { f) } \frac{a^{a+b+c}}{a^{2 a-2 b+c}} \\ \text { g) } 4^{x} \times 8^{x+1} & \text { h) } \frac{9^{x}}{27^{x-1}} \\ \text { i) } \frac{5^{2 n+1} \times 3^{2 n-3}}{3^{2 n} \times 5^{2 n}} & \text { j) } \frac{5^{2 n+1} \times 5^{2 n-2} \times 5}{25^{2 n-1}} \\ \text { k) } \frac{12^{n+1} \times 9^{2 n-1}}{36^{n} \times 8^{1-n}} & \text { l) } \frac{5^{2 n} \times 15^{n-1} \times 3^{n}}{125^{n} \times 3^{n-1}} \\ \text { m) } \frac{27^{n-2} \times 6^{n}}{162^{n}} & \text { n) } \frac{10^{n} \times 25^{n-1} \times 2}{50^{n+1}} \\ \text { o) } \frac{12^{x} \times 9^{x+1}}{4^{x-1} \times 27^{x}} & \text { p) } \frac{20^{x+1} \times 4^{x}}{16^{x-1} \times 5^{x}} \\ \text { 2. Multiply. } & \text { b) } y\left(y^{-1}-2\right) \\ \text { a) } x^{2}\left(x^{3}+1\right) & \text { d) } 3^{x+1}\left(3^{x}-3^{2}\right) \\ \text { c) } 2^{n}\left(2^{n}+1\right) & \\ \text { Eind } & \text { it }\end{array} \)

Ask by Rowe Williams. in South Africa
Mar 16,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

**Simplified Expressions:** a) \(2\) b) \(\frac{506250}{6889}\) c) \(\frac{1}{2}\) d) \(3^{3 - n}\) e) \(2^{m}\) f) \(a^{-a + 3b}\) g) \(2^{5x + 3}\) h) \(3^{3 - x}\) i) \(\frac{5}{27}\) j) \(25\) k) \(\frac{12^{n+1} \times 9^{2n-1}}{36^{n} \times 8^{1-n}}\) (Further simplification required) **Multiplication:** a) \(x^{5}\) b) \(y^{-1} - 2y\) c) \(2^{2n}\) d) \(3^{2x} - 3^{x+1}\)

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

Beyond the Answer

To solve these expressions, a strong foundational understanding of exponents and how to manipulate them is essential. Remember, when you multiply like bases, you add the exponents, and when you divide, you subtract them. This can transform complex-looking fractions into much simpler forms. For example, in expression (a), simplify \(20\) and \(25\) into their prime factorizations to reduce the expression effectively. In terms of practical application, simplifying expressions with exponents and multiplication is incredibly useful in fields like engineering and finance, where you often need to analyze growth rates, interest calculations, and more without getting bogged down by cumbersome calculations. Seamless simplifications save time and minimize errors, allowing you to focus on interpreting the results accurately.

Related Questions

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