Could someone check my work please? Thank you!
(14a^2b)(2ab^2c) = 28a^3b^3c
(a^25)^7 = a^125
6x^6 ∙ 6x^6 = 36^12
(2x^2)^3 = 8x^6
(-2)0 = 1
30x^20/(6x^9 = 5x^11
4x^5 ∙ 6x^6 = 24x^11
(2x^4)^3 = 8x^12
-4^2 = -16
-(193)^0 = -1
(-193)0 = 1
(-5)2 = 25
((6x^7)/(2x^2 ))^2 = 9x^45???????
(-6x&6)(-6x^2x^6) -- I have no idea how to solve this one. HELP PLEASE!
(14a^2b)(2ab^2c) = 28a^3b^3c ✔
(a^25)^7 = a^125 ✔
6x^6 ∙ 6x^6 = 36^12 no,
keep the base and add the exponents = 6^12
or multiply the bases and keep the same exponent = 36^6
(2x^2)^3 = 8x^6 ✔
(-2)^0 = 1 ✔
30x^20/(6x^9 = 5x^11 ✔
4x^5 ∙ 6x^6 = 24x^11 ✔
(2x^4)^3 = 8x^12 ✔
-4^2 = -16 ✔
-(193)^0 = -1 ✔
(-193)^0 = 1 ✔
(-5)2 = 25 ✔
((6x^7)/(2x^2 ))^2 = 9x^45??????? NO
= (3x^5)^2
= 9x^10
(-6x&6)(-6x^2x^6) , you meant (-6x^6)(-6x^2x^6)
= 36x^14
=
6x^6 ∙ 6x^6 = 36^12 no,
keep the base and add the exponents = 6^12
or multiply the bases and keep the same exponent = 36^6
Why would this be? I thought I had to multiply the 6 in each and then add the exponents in each?
((6x^7)/(2x^2 ))^2 = 9x^45??????? NO
= (3x^5)^2
= 9x^10
I re-did this one before you responded and got this answer also.
(-6x&6)(-6x^2x^6) , you meant (-6x^6)(-6x^2x^6)
= 36x^14
=
I also re-did this one and got this but with the extra = sign are you saying there is more to simplify because I thought this would be the final answer.
Thanks so much - I'm just trying to make certain I understand this.
6x^6 ∙ 6x^6 = 36^12
Your answer is wrong, should be
36x^12
looks like you missed the x
and for some reason I thought you multiplied the bases of 6 and added the exponents.
In the last question, the last = sign
is just a stray one hanging around, ignore it.
Reiny, thanks but the original problem isn't (-6x^6)(6x^6)
The original problem is (-6x^6)(-6x^2x^6)
So I thought I would have to simplify inside the second parentheses first to make that (-6x^8) by adding the exponents (2 + 6)
Then I have (-6x^6)(-6x^8)
I then multiply -6 x -6 = 36
and then add the exponents to get 36x^14
To check each of the expressions, we need to simplify them and compare the result to the given answer. Let's go through each one step by step:
1. (14a^2b)(2ab^2c) = 28a^3b^3c
To multiply the terms, we multiply the coefficients and add the exponents for each variable: 14 * 2 = 28, a^2 * a = a^3, b * b^2 = b^3, and c remains as c. The result matches the given answer, so it is correct.
2. (a^25)^7 = a^125
To raise an exponent to another exponent, we multiply the exponents: 25 * 7 = 175. The result does not match the given answer, so it is incorrect.
3. 6x^6 ∙ 6x^6 = 36^12
To multiply the terms, we multiply the coefficients and add the exponents for x: 6 * 6 = 36, and 6 + 6 = 12. The result matches the given answer, so it is correct.
4. (2x^2)^3 = 8x^6
To raise a term to an exponent, we raise each factor to that exponent: (2^3) * (x^2)^3 = 8x^6. The result matches the given answer, so it is correct.
5. (-2)^0 = 1
Any number raised to the power of 0 is equal to 1. The result matches the given answer, so it is correct.
6. 30x^20/(6x^9) = 5x^11
To divide the terms, we divide the coefficients and subtract the exponents for x: 30/6 = 5, and 20 - 9 = 11. The result matches the given answer, so it is correct.
7. 4x^5 ∙ 6x^6 = 24x^11
To multiply the terms, we multiply the coefficients and add the exponents for x: 4 * 6 = 24, and 5 + 6 = 11. The result matches the given answer, so it is correct.
8. (2x^4)^3 = 8x^12
To raise a term to an exponent, we raise each factor to that exponent: (2^3) * (x^4)^3 = 8x^12. The result matches the given answer, so it is correct.
9. -4^2 = -16
In this expression, the exponent applies only to the number, not the negative sign: -4^2 = -(4^2) = -16. The result matches the given answer, so it is correct.
10. -(193)^0 = -1
Any number raised to the power of 0 is equal to 1, but in this expression, the negative sign is included: -(193)^0 = -1. The result matches the given answer, so it is correct.
11. (-193)^0 = 1
Any number raised to the power of 0 is equal to 1. The result matches the given answer, so it is correct.
12. (-5)^2 = 25
In this expression, the exponent applies to the negative sign and the number: (-5)^2 = 25. The result matches the given answer, so it is correct.
13. ((6x^7)/(2x^2))^2 = 9x^45
To simplify the expression inside the parentheses, divide the coefficients and subtract the exponents for x: (6/2) * (x^7/x^2) = 3 * x^(7-2) = 3x^5. Then, raise the simplified term to the power of 2: (3x^5)^2 = 9x^(5*2) = 9x^10. The result does not match the given answer, so it is incorrect.
14. (-6x^6)(-6x^2x^6)
To multiply the terms, we multiply the coefficients and add the exponents for x: (-6) * (-6) = 36, and 6 + 2 + 6 = 14. The result is 36x^14.