Simplify Scientific Notation: 10×10^-3×10^5 Multiplication Problem

Reduce the following equation:

10×10−3×105= 10\times10^{-3}\times10^5=

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Simplify the following problem
00:04 Any number raised to the power of 1 is always equal to itself
00:08 We'll apply this formula to our exercise, and raise to the power of 1
00:11 According to the laws of exponents, the multiplication of powers with equal bases (A)
00:14 equals the same base raised to the sum of the exponents (N+M)
00:17 We'll apply this formula to our exercise
00:20 Note that we're adding a negative factor
00:36 A positive x A negative is always negative, therefore we subtract as follows
00:48 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Reduce the following equation:

10×10−3×105= 10\times10^{-3}\times10^5=

2

Step-by-step solution

To simplify the equation 10×10−3×105 10 \times 10^{-3} \times 10^5 , we will apply the exponent multiplication rule which states that when multiplying like bases, we add the exponents.

  • Step 1: Identify exponents on each term - The base for all terms is 1010.
  • Step 2: The expression can be rewritten using implied exponents:
    101×10−3×105 10^1 \times 10^{-3} \times 10^5
  • Step 3: Apply the rule of exponents. When multiplying terms with the same base, add the exponents:
    101+(−3)+5 10^{1 + (-3) + 5}
  • Step 4: Calculate the sum of the exponents:
    1+(−3)+5=3 1 + (-3) + 5 = 3
  • Step 5: Rewrite the expression with the summed exponent:
    103 10^3

Therefore, the simplified expression is 103 10^3 , which is choice 4.

3

Final Answer

103 10^3

Practice Quiz

Test your knowledge with interactive questions

\( 112^0=\text{?} \)

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Exponents Rules questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations

Multiplication of Powers

Simplify 8^(-10) × 8^5 × 8^4: Exponent Reduction Problem
Click to solve
Simplify 3^(-2) × 3^4: Combining Negative and Positive Exponents
Click to solve