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Expressions with Exponents

Grade 6 · Algebra · Worksheet 1

  1. 5³ + 10² = ? Answer: ______________
  2. Noah is designing a square-shaped community garden. Each side of the garden will measure 9 meters. He wants to know the total area of the garden in square meters. Write an expression using an exponent to represent the area, then evaluate it. Answer: ______________
  3. Hana is designing a square mosaic for a school art project. She draws a square on a coordinate grid with corners at (11, 7), (19, 7), (19, 15), and (11, 15). Inside the square, she places a small circular tile at the center with a radius of 2 units. Hana wants to cover the area of the square not covered by the circle with tiny glass beads. What is the area that needs to be covered with beads? (Use π = 3.14)
    Answer: ______________
  4. Mason is designing a square tile mosaic. The side length of the square mosaic is 9 tiles. He then decides to add a smaller square in the center with a side length of 4 tiles. Write an expression using exponents to represent the total number of tiles in the large square minus the tiles in the small square, then evaluate it to find how many tiles are in the border region. Answer: ______________
  5. (-5)² - 3 × (12 - 15) ÷ 3 = ? Answer: ______________
  6. (-5)² - 3 × (15 - 20) ÷ 3 = ? Answer: ______________
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Answer Key & Explanations

Expressions with Exponents · Grade 6 · Worksheet 1

  1. 5³ + 10² = ? Answer: 225 Solution: Evaluate 5³. This means 5 × 5 × 5. 5 × 5 = 25, then 25 × 5 = 125.
    Full step-by-step solution

    Step 1: Evaluate 5³. This means 5 × 5 × 5. 5 × 5 = 25, then 25 × 5 = 125. Step 2: Evaluate 10². This means 10 × 10 = 100. Step 3: Add the results: 125 + 100 = 225. The answer is 225.

  2. Noah is designing a square-shaped community garden. Each side of the garden will measure 9 meters. He wants to know the total area of the garden in square meters. Write an expression using an exponent to represent the area, then evaluate it. Answer: 81 Solution: The area of a square is side length times side length. Here, the side length is 9 meters. Write the expression: 9 squared, or 9^2.
    Full step-by-step solution

    Step 1: The area of a square is side length times side length. Here, the side length is 9 meters. Step 2: Write the expression: 9 squared, or 9^2. Step 3: Evaluate: 9^2 = 9 × 9 = 81. The area of the garden is 81 square meters.

  3. Hana is designing a square mosaic for a school art project. She draws a square on a coordinate grid with corners at (11, 7), (19, 7), (19, 15), and (11, 15). Inside the square, she places a small circular tile at the center with a radius of 2 units. Hana wants to cover the area of the square not covered by the circle with tiny glass beads. What is the area that needs to be covered with beads? (Use π = 3.14) Answer: 51.44 Solution: Find the side length of the square. The corners are at (11, 7), (19, 7), (19, 15), and (11, 15). The side length along the x-axis is 19 - 11 = 8 units.
    Full step-by-step solution

    Step 1: Find the side length of the square. The corners are at (11, 7), (19, 7), (19, 15), and (11, 15). The side length along the x-axis is 19 - 11 = 8 units. The side length along the y-axis is 15 - 7 = 8 units. So the square has side length 8 units. Step 2: Find the area of the square. Area = side × side = 8 × 8 = 64 square units. Step 3: Find the center of the square. The center is halfway between the x-coordinates and the y-coordinates. x-center = (11 + 19)/2 = 30/2 = 15. y-center = (7 + 15)/2 = 22/2 = 11. So the center is at (15, 11). This is where the circular tile is placed. Step 4: Find the area of the circular tile. Radius = 2 units. Area of circle = π × r^2 = 3.14 × (2)^2 = 3.14 × 4 = 12.56 square units. Step 5: Find the area to be covered with beads. Area for beads = Area of square - Area of circle = 64 - 12.56 = 51.44 square units. The answer is 51.44.

  4. Mason is designing a square tile mosaic. The side length of the square mosaic is 9 tiles. He then decides to add a smaller square in the center with a side length of 4 tiles. Write an expression using exponents to represent the total number of tiles in the large square minus the tiles in the small square, then evaluate it to find how many tiles are in the border region. Answer: 65 Solution: Write the expression for the large square area: 9^2. Write the expression for the small square area: 4^2. The border area is the difference: 9^2 - 4^2.
    Full step-by-step solution

    Step 1: Write the expression for the large square area: 9^2. Step 2: Write the expression for the small square area: 4^2. Step 3: The border area is the difference: 9^2 - 4^2. Step 4: Evaluate: 9^2 = 81, 4^2 = 16. Step 5: Subtract: 81 - 16 = 65. The border region contains 65 tiles.

  5. (-5)² - 3 × (12 - 15) ÷ 3 = ? Answer: 28 Solution: Calculate the exponent: (-5)² = 25 Calculate inside parentheses: (12 - 15) = -3 Perform multiplication: 3 × (-3) = -9 Perform division: -9 ÷ 3 = -3 Subtract: 25 - (-3) = 25 + 3 = 28 The answer is 28.
    Full step-by-step solution

    Step 1: Calculate the exponent: (-5)² = 25 Step 2: Calculate inside parentheses: (12 - 15) = -3 Step 3: Perform multiplication: 3 × (-3) = -9 Step 4: Perform division: -9 ÷ 3 = -3 Step 5: Subtract: 25 - (-3) = 25 + 3 = 28 The answer is 28.

  6. (-5)² - 3 × (15 - 20) ÷ 3 = ? Answer: 30 Solution: Calculate the exponent: (-5)² = 25 Calculate inside parentheses: (15 - 20) = -5 Perform multiplication and division from left to right: 3 × (-5) = -15 Continue division: -15 ÷ 3 = -5 Perform subtraction: 25 - (-5) = 25 + 5 = 30 The answer is 30.
    Full step-by-step solution

    Step 1: Calculate the exponent: (-5)² = 25 Step 2: Calculate inside parentheses: (15 - 20) = -5 Step 3: Perform multiplication and division from left to right: 3 × (-5) = -15 Step 4: Continue division: -15 ÷ 3 = -5 Step 5: Perform subtraction: 25 - (-5) = 25 + 5 = 30 The answer is 30.