This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You're on a roll — here are the solutions to the math problems: 4) For 3^2, identify: a. the base number. b. the exponent. a. The base number is the number being multiplied by itself. Base number: 3 b. The exponent is the number of times the base is multiplied by itself. Exponent: 2 5) Colour all the square numbers on the multiplication board. What pattern do you see? Square numbers are the result of multiplying a number by itself (n × n). The square numbers on the multiplication board are: 1 × 1 = 1 2 × 2 = 4 3 × 3 = 9 4 × 4 = 16 5 × 5 = 25 6 × 6 = 36 7 × 7 = 49 8 × 8 = 64 9 × 9 = 81 10 × 10 = 100 These numbers form a diagonal pattern from the top-left corner to the bottom-right corner of the multiplication board. 6) Arrange these numbers in ascending order: 2, 9^2, 5^2, 5, 6^2, 2^2, 8^2, 7^2, 1^2, 1^3, 10, 11^2, 4^2, 10^2 Step 1: Calculate the value of each number. 2 = 2 9^2 = 9 × 9 = 81 5^2 = 5 × 5 = 25 5 = 5 6^2 = 6 × 6 = 36 2^2 = 2 × 2 = 4 8^2 = 8 × 8 = 64 7^2 = 7 × 7 = 49 1^2 = 1 × 1 = 1 1^3 = 1 × 1 × 1 = 1 10 = 10 11^2 = 11 × 11 = 121 4^2 = 4 × 4 = 16 10^2 = 10 × 10 = 100 The list of values is: 2, 81, 25, 5, 36, 4, 64, 49, 1, 1, 10, 121, 16, 100. Step 2: Arrange the values in ascending order (smallest to largest). 1, 1, 2, 4, 5, 10, 16, 25, 36, 49, 64, 81, 100, 121 Step 3: Write the original numbers in ascending order. 1^2, 1^3, 2, 2^2, 5, 10, 4^2, 5^2, 6^2, 7^2, 8^2, 9^2, 10^2, 11^2 7) Arrange the above numbers in descending order: To arrange in descending order, we take the ascending list and reverse it. 11^2, 10^2, 9^2, 8^2, 7^2, 6^2, 5^2, 4^2, 10, 5, 2^2, 2, 1^3, 1^2 8) Fill in <, > or = a. 2^2 \_ 2 × 2 2^2 = 4 2 × 2 = 4 So, 4 = 4 2^2 = 2 × 2 b. 5^2 \_ 5 × 2 5^2 = 25 5 × 2 = 10 So, 25 > 10 5^2 > 5 × 2 c. 9^2 \_ 9 × 9 9^2 = 81 9 × 9 = 81 So, 81 = 81 9^2 = 9 × 9 d. 8^2 \_ 2 × 8 8^2 = 64 2 × 8 = 16 So, 64 > 16 8^2 > 2 × 8 e. 11^2 \_ 10 × 11 11^2 = 121 10 × 11 = 110 So, 121 > 110 11^2 > 10 × 11 f. 3 × 3 \_ 3^2 3 × 3 = 9 3^2 = 9 So, 9 = 9 3 × 3 = 3^2 9) Numbers which have an exponent of 2 are called square numbers. What's next?