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What is the definition of the word "base" when the mathematical expression contains an exponent?(1 point)

Responses

The base is the number that tells you how many times to multiply by itself.
The base is the number that tells you how many times to multiply by itself.

The base is the biggest number in the expression.
The base is the biggest number in the expression.

The base is the number that tells you to square a number.
The base is the number that tells you to square a number.

The base is the number being multiplied by itself a given number of times.
The base is the number being multiplied by itself a given number of times.

Put the simplified expressions in order on the number line from least to greatest.

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(4 points)
2(6)-2(4)/2(2)
1/4(-2)
(1/2)(-3)
(-2)(-8) . (-2)(11)

1 answer

Definition of "base" in Mathematics:

The correct definition of the word "base" in the context of mathematical expressions containing an exponent is:

The base is the number being multiplied by itself a given number of times.

Ordering Simplified Expressions on the Number Line:

  1. Simplify each expression:

    • \(2(6) - 2(4)/2(2)\)

      • \(2(6) = 12\)
      • \(2(4) = 8\)
      • \(2(2) = 4\)
      • Therefore, \(12 - 8/4 = 12 - 2 = 10\)

    • \(1/4(-2) = -2/4 = -1/2 = -0.5\)

    • \((1/2)(-3) = -3/2 = -1.5\)

    • \((-2)(-8) \cdot (-2)(11)\)

      • The first part: \((-2)(-8) = 16\)
      • The second part: \((-2)(11) = -22\)
      • So, \(16 \cdot (-22) = -352\)

  2. List the simplified results:

    • \(10\)
    • \(-0.5\)
    • \(-1.5\)
    • \(-352\)

  3. Order from least to greatest:

    • \(-352\)
    • \(-1.5\)
    • \(-0.5\)
    • \(10\)

Final Order:

  • \(-352, -1.5, -0.5, 10\)