Question
upstudy study bank question image url

4.3 Calculate the following without the use of a calculator: \( \begin{array}{l}4.3 .1 \\ -2+(-4)(-2)-3 \\ 4.3 .2 \\ 8+9 \times 10 \div(3+7) \\ 4.3 .3\end{array} 3^{3}-11^{2}+\sqrt[4]{-256}-(-5)^{3} \)

Ask by Montgomery Flynn. in South Africa
Mar 12,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

**4.3.1** \[ -2 + (-4)(-2) - 3 = 3 \] **4.3.2** \[ 8 + 9 \times 10 \div (3+7) = 17 \] **4.3.3** \[ 3^{3} - 11^{2} + \sqrt[4]{-256} - (-5)^{3} = 31 + 2\sqrt{2} + 2\sqrt{2}i \]

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

Bonus Knowledge

Let's tackle each part step by step! For the first calculation: \(-2 + (-4)(-2) - 3\) This simplifies as follows: 1. \((-4)(-2) = 8\) 2. Now, substitute back: \(-2 + 8 - 3\) 3. Combine: \(6 - 3 = 3\) Now onto the second part: \(8 + 9 \times 10 \div (3 + 7)\) 1. Calculate \(3 + 7 = 10\) 2. Now calculate \(9 \times 10 = 90\) 3. Then divide by \(10\): \(90 \div 10 = 9\) 4. Finally, add: \(8 + 9 = 17\) For the last part: \(3^{3} - 11^{2} + \sqrt[4]{-256} - (-5)^{3}\) 1. Calculate \(3^3 = 27\) 2. Calculate \(11^2 = 121\) 3. Now, we encounter \(\sqrt[4]{-256}\). This is not a real number because the fourth root of a negative number is not real; it's imaginary. Hence we can say it’s \(0\) in the context of real numbers if you're simplifying. 4. Now \(-(-5^3)= -(-125) = 125\) 5. Putting it all together gives us \(27 - 121 + 0 + 125\) 6. Combine: \(27 + 125 = 152\), then \(152 - 121 = 31\) So the final results are: 4.3 .1: \(3\) 4.3 .2: \(17\) 4.3 .3: \(31\)

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