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

Question

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

Answer 1

#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.

Answer 2

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.

Answer 3

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

Answer 4

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