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
#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.
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.
I am confused. Both of you has written different answers to many of the questions I have answered incorrectly. Which is correct?
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
To evaluate each expression for the given value(s) of the variable(s), you need to substitute the value(s) into the expression and simplify.
1. t^6 for t = 2
To evaluate t^6 for t = 2, substitute 2 for t in the expression: (2)^6
This simplifies to 64.
Answer: 64
2. r^0s^-2 for r = 8 and s = 10
To evaluate r^0s^-2 for r = 8 and s = 10, substitute 8 for r and 10 for s in the expression: (8)^0 * (10)^(-2)
Any number raised to the power of 0 equals 1, so r^0 becomes 1. (8)^0 = 1
(10)^(-2) means the reciprocal of 10 squared, which is 1/10^2 = 1/100
So the expression simplifies to 1 * 1/100 = 1/100.
Answer: 1/100
3. x^4/x^-6
To simplify x^4/x^-6, you can use the rule of dividing powers with the same base by subtracting the exponents: x^(4 - (-6)) = x^4 * x^6 = x^(4 + 6) = x^10
Answer: x^10
4. a^-3/b^-2
To simplify a^-3/b^-2, you can use the rule of dividing powers with the same base by subtracting the exponents: a^(-3 - (-2)) / b^-2 = a^(-3 + 2) / b^-2 = a^-1 / b^-2
When a negative exponent is in the numerator, it becomes a positive exponent in the denominator, and vice versa. So, a^-1 becomes 1/a^1 = 1/a, and b^-2 becomes 1/b^2.
Therefore, the expression simplifies to 1/a * 1/b^2 = 1/(ab^2).
Answer: 1/(ab^2)
5. The lead in a mechanical pencil has a diameter of 0.5 mm. Write this number in scientific notation.
To write 0.5 mm in scientific notation, you need to express it as a number between 1 and 10, multiplied by a power of 10.
0.5 mm can be written as 5 x 10^(-1) = 5 x 0.1 = 0.5 (since 10^(-1) = 0.1)
Answer: 0.5 x 10^(-1)
6. 3^5 x 3^-3
To simplify 3^5 x 3^-3, you can use the rule of multiplying powers with the same base by adding the exponents: 3^(5 + (-3)) = 3^2
Answer: 3^2
7. a^3 x a^-6 x a^-2
To simplify a^3 x a^-6 x a^-2, you can apply the commutative property of multiplication to rearrange the terms: a^3 x a^-6 x a^-2 = a^3 x a^-2 x a^-6
Then, you apply the rule of multiplying powers with the same base by adding the exponents: a^(3 + (-2) + (-6)) = a^-5
Answer: a^-5
8. (3x^4)^3
To simplify (3x^4)^3, you need to raise both 3 and x^4 to the exponent 3: 3^3 x (x^4)^3 = 27 x^12
Answer: 27 x^12
9. (-4d^7)^2
To simplify (-4d^7)^2, you need to square both -4 and d^7: (-4)^2 x (d^7)^2 = 16d^14
Since (-4)^2 = 16, and when you raise a power to another exponent, you multiply the exponents: (d^7)^2 = d^(7 x 2) = d^14
Therefore, the expression simplifies to 16d^14.
Answer: 16d^14