Algebra 1 Answer Evaluation (Reiny)

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Evaluate each expression for the given value(s) of the variable(s).

1. t^6 for t = 2

A: 1/64

2. r^0s^-2 for r = 8 and s = 10

A: 1/100?

Simplify.

3. x^4/x^-6

A: 1/x^4y^6? Or x^4y^6?

4. a^-3/b^-2

A: 1/a^3b^2? Or a^3b^2?

5. The lead in a mechanical pencil has a diameter of 0.5 mn. Write this number in scientific notation.

A: ?

Simplify.

6. 3^5 x 3^-3

A: 3^2

7. a^3 x a^-6 x a^-2

A: a^15

8. (3x^4)^3

A: 27x^12

9. (-4d^7)^2

A: -16d^14

  • Algebra 1 Answer Evaluation (Reiny) -

    #1. Nope 2^6 = 64 (2*2*2*2*2*2)
    2^-6 = 1/2^6 = 1/64

    #2 ok

    #3 where did the y's come from? When dividing, subtract exponents
    x^4/x^-6 = x^(4-(-6)) = x^10

    #4 negative exponents indicate reciprocals. As a shortcut, they mean the item switches top and bottom in a fraction

    a^-3/b^-2 = b^2/a^3

    #5 0.5 = 5.0x10^-1

    #6 ok

    #7 nope. add the exponents when multiplying

    a^(3-6-2) = a^-5

    #8 ok

    #9 nope.
    (-4)^2 = (-4)(-4) = +16
    -4^2 = -(4^2) = -16

    powers are done before subtraction unless parentheses change the order.

  • Algebra 1 Answer Evaluation (Reiny) -

    1. 2^4 = 64 , not 1/64
    2. ok
    3. x^4 y^6 , your first choice is incorrect
    4. a^-3/b^-2 = a^(-3 -(-2)) = a^-1 or 1/a
    5. 0.5 = 5.0 x 10^-1
    6. 3^2 = 9 , they probably want the actual answer
    7. a^3 x a^-6 x a^-2 = a^-5 or 1/a^5 , notice 3-6-2=-5
    8. ok
    9. (-4d^7)^2 = +16 d^14

    looks like some further review is needed.

  • Algebra 1 Answer Evaluation (Reiny) -

    I am confused. Both of you has written different answers to many of the questions I have answered incorrectly. Which is correct?

  • Algebra 1 Answer Evaluation (Reiny) -

    I messed up in #3 and #4

    #3, I looked at your answer and saw the y's, should have looked at the original question which had no y values.
    answer is x^10 , see Steve's

    #4.
    a^-3/b^-2 = b^2/a^3, see Steve's

    We have the same answers for the rest

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