1: -(5)^-1
A: -1/5
B: -5
C: 5 *****
D: 1/5
2; (-4.7) ^0
A: 1***
B: -1
C: 0
D: -4.7
3:
-1/p^-6
A: -6/p-6
B: -6p ****
C: -p^6
D: p^6
4: 6^3 x 6^10
A: 36^13
B: 6^13
C: 6^30 *****
D: 18^30
Simplify this expression (-4) ^-6 (-4) ^7
A: 4^13
B:-4 *****
C: 13
D: 1
I just need it to be checked please.
#1 no
#2 yes
#3 no
#4 no
#5 yes
looks like somebody needs more review and exercises.
#1. negative exponents mean reciprocals.
-(5)^-1 = -(1/5) = -1/5
#2. ok
#3. again with the negative exponents...
-1/p^-6 = -1 / (1/p^6) = -1*p^6 = -p^6
You can think of negative exponents as switching a number between top and bottom of a fraction, and changing between plus and minus (the exponent only!)
x^-6 = x^06/1 = 1/x^6
1/y^2 = y^-2
1/y^-2 = y^2
#4. when multiplying numbers, add powers
6^3 x 6^10 = 6^13
It's just a shorthand way of writing 6*6*6 * 6*6*6*6*6*6*6*6*6*6 = 6^13
what you did was
(6^3)^10 = (6*6*6) ... 10 times = 6^30
you multiply the exponents when raising a power to a power
#5. correct
Though I wonder whether it was an accident, given your mistakes above. Too bad you didn't show any work ...
1: To simplify -(5)^-1, we can apply the rule that states a negative exponent can be rewritten as the reciprocal of the positive exponent.
Step 1: Rewrite -(5)^-1 as -1/(5)^1. The negative exponent becomes the reciprocal of the positive exponent.
Step 2: Simplify -1/(5)^1 as -1/5.
Therefore, the answer is A: -1/5.
2: To simplify (-4.7)^0, we need to understand that any number raised to the power of 0 is equal to 1.
Therefore, the answer is A: 1.
3: To simplify -1/p^-6, we need to apply the rule that states a negative exponent can be rewritten as the reciprocal of the positive exponent.
Step 1: Rewrite -1/p^-6 as -1/(1/p^6). The negative exponent becomes the reciprocal of the positive exponent.
Step 2: Simplify -1/(1/p^6) as -1 * p^6/1. Multiplying by the reciprocal allows us to eliminate the fraction.
Step 3: Simplify -1 * p^6/1 as -p^6.
Therefore, the answer is C: -p^6.
4: To simplify 6^3 x 6^10, we can apply the rule that states when multiplying numbers with the same base, we add their exponents.
Step 1: Add the exponents of 6, which are 3 and 10. 3 + 10 = 13.
Step 2: Rewrite the expression as 6^13.
Therefore, the answer is B: 6^30.
Simplify this expression (-4)^-6 x (-4)^7:
To simplify this expression, we need to apply the rule that states when multiplying numbers with the same base, we add their exponents.
Step 1: Add the exponents of -4, which are -6 and 7. (-6) + 7 = 1.
Step 2: Rewrite the expression as (-4)^1.
Therefore, the answer is B: -4.