i need help. not saying these are right, i just tried my best, could someone check them for me? (NOT ALL ARE ANSWERED)
1. (-5)^-1
A. - 1/5 **********
B. -5
C. 5
D. 1/5
2. (-8.3) ^0
A. 1
B. -1
C. 0
D. -8.3 **********
3. -1/a^-2
A. -a^2
B. -2/a
C.-2a
D. a^2 **********
4. 4^6 * 4^3
A. 4^9 **********
B. 4^18
C. 12^9
D. 64^9
5. (3)^10 (3)^-9
A. 3
B. 1/3
C. 9^-90 **********
D. 9
6. (y^6)^2
A. 2y^12
B. y^12 **********
C. y^8
D. y^36
7. (6q^6)^-4
A. 6q^1296
B. 1296q^2
C. 1/1296 q^24
D. 6q^-24 **********
8. What is the value of 11x^-3 y^-1 for x= -1 and y=2
A. -2/11
B. -22
C. -66
D. -11/2
(yikes i dont know this one...)
9. (t^-4)^-9 t^2
A. t^26
B. t^-26 **********
C. t^38
D. t^-38
10. (4/7y^5) ^2
A. 8 / 14y^10
B. 16/ 49 y^25
C. 16/9^10
D. 8/14 y^25
11. Determine if the number 3.14*10^-6 is written in scientific notation. If not, explain.
A. Yes; the number is written in scientific notation **********
B. No; the first number is not a number between 1 and 10
C. No; it is not written as a number times a power of 10
There is 23 questions overall but I will submit in the rest once I try to finish and see if anyone is able to help me here.
#1 , yes
#2
sorry, pressed submit too soon
#2 , no, anything ^0 = 1
#3, no, -1/a^-2 = -1(a^2) or -a^2
#4 yes
#5 ,no , same kind as #4, why did you go off very strange here?
(3)^10 (3)^-9 = 3^1 or 3
#6 yes
#7 no, (6q^6)^-4 = (6^-4)(q^6)^-4
= (1/1296)(q^-24)
=1/(1296q^24) which is C
#8 11x^-3 y^-1 = 11(1/x^3)(1/y) = 11(1/(-1)^3 )(1/2) = 11(-1)(1/2) = -11/2
#9 no , (t^-4)^-9 t^2 = t^36 t^2= t^38
#10 ??? , very easy (4/7y^5) ^2 = (16/49)y^10
#11 yes,
4/11 is not close to competency. Looks like somebody has to spent
some more time on this.
Correct answer:
1.
4.
6.
and
11
Wrong answers:
2. ( - 8.3 )⁰ = 1
Any number to zero power is equal one.
3.
a⁻² = 1 / a²
so
- 1 / a⁻² = - 1 / ( 1 / a² ) = - 1 ∙ a² = - a²
5.
aᵐ ∙ aⁿ = aᵐ⁺ⁿ
3¹⁰ ∙ 3⁻⁹ = 3¹⁰⁻⁹ = 3¹ = 3
7.
( aᵐ )ⁿ = aᵐ ⁿ
( 6 q⁶ )⁻⁴ = 6⁻⁴ ∙ ( q⁶ )⁻⁴ = 1 / 6⁴ ∙ q²⁴ = 1 / 6⁴ ∙ q²⁻⁴ = 1 / 1296 ∙ 1 / q²⁴ = 1 / 1296 q²⁴
8.
11 x⁻³ ∙ y⁻¹ = 11 ∙ 1 / x³ ∙ 1 / y¹ = 11 / x³ ∙ y
Put x = - 1 and y = 2 in this expression
11 / (- 1)³ ∙ 2 = 11 / (- 1) ∙ 2 = 11 / - 2 = - 11 / 2
9.
( t⁻⁴ )⁻⁹ ∙ t² = ( t )⁻⁴ * ⁻⁹ ∙ t² = t³⁶ ∙ t² = t³⁶⁺² = t³⁸
10.
( 4 / 7 y⁵ )² = ( 4 / 7 )² ∙ ( y⁵ )² = 4² / 7² ∙ y⁵*² = 16 / 49 ∙ y¹⁰
Sure! I can help you check your answers and explain how to get the correct answer for each question.
1. (-5)^-1
To calculate this, we use the exponent rule where a negative exponent is equal to one divided by the base raised to the positive exponent. So, (-5)^-1 is the same as 1/(-5)^1, which is equal to -1/5. Therefore, the correct answer is A. -1/5.
2. (-8.3) ^0
Any number raised to the power of 0 is always equal to 1. Therefore, the correct answer is A. 1.
3. -1/a^-2
To solve this, we can apply the exponent rule for negative exponents. a^-2 is the same as 1/a^2. Multiplying -1 with 1/a^2 gives -1/a^2, therefore the correct answer is D. a^2.
4. 4^6 * 4^3
When multiplying exponential expressions with the same base, you add the exponents. So, 4^6 * 4^3 is equal to 4^(6+3), which simplifies to 4^9. Therefore, the correct answer is A. 4^9.
5. (3)^10 (3)^-9
Similar to the previous question, when multiplying exponential expressions with the same base, you add the exponents. In this case, we have (3)^10 (3)^-9, which simplifies to 3^(10+(-9)). The sum of 10 and -9 is 1. Therefore, the correct answer is A. 3^1 or simply 3.
6. (y^6)^2
When raising a power to another power, you multiply the exponents. In this case, we have (y^6)^2, which simplifies to y^(6*2) or y^12. Therefore, the correct answer is B. y^12.
7. (6q^6)^-4
To solve this, we can apply the exponent rule for negative exponents. (6q^6)^-4 is the same as 1/(6q^6)^4. Squaring the base and multiplying the exponents gives us 1/(6^4 * (q^6)^4), which simplifies to 1/(1296 * q^24). Therefore, the correct answer is C. 1/1296 q^24.
8. To find the value of 11x^-3 y^-1 for x = -1 and y = 2, we replace x and y with their respective values in the expression.
So, substituting x = -1 and y = 2, we get 11*(-1)^-3*(2)^-1.
Since (-1)^-3 is equal to -1 and (2)^-1 is equal to 1/2, the expression simplifies to 11 * (-1) * (1/2), which is equal to -11/2.
Therefore, the correct answer is D. -11/2.
9. (t^-4)^-9 t^2
To solve this, we can apply the exponent rule for negative exponents. (t^-4)^-9 is the same as 1/(t^(-4 * -9)), which simplifies to 1/t^36. Multiplying this result with t^2 gives us t^2/t^36, which simplifies to t^(2-36) or t^-34.
Therefore, the correct answer is B. t^-26.
10. (4/7y^5) ^2
To square this expression, we square both the numerator and the denominator separately. (4/7y^5)^2 becomes (4^2)/(7^2 * (y^5)^2), which simplifies to 16/(49 * y^10).
Therefore, the correct answer is B. 16/49 y^10.
11. Determine if the number 3.14*10^-6 is written in scientific notation.
Scientific notation is written as a number between 1 and 10, multiplied by a power of 10. In this case, 3.14*10^-6 can be written as 3.14 * (10^-6). Since 3.14 is a number between 1 and 10, and it is multiplied by a power of 10, the number 3.14*10^-6 is indeed written in scientific notation.
Therefore, the correct answer is A. Yes; the number is written in scientific notation.
I hope this helps! Let me know if there's anything else I can assist you with.