Consider the numerical expression: 3^4
part a: If the given expression is raised to the power of 12, which expression is NOT equivalent? Options: 3^16, 3^48, (3^12)^4, or (3^6)^8.
part b: If the given expression is multiplied by 3^6, which expression is NOT equivalent? options: 3^10, 9^10, (3^5)(3^5), or (3^2)(3^8).
Part a:
To find which expression is NOT equivalent to 3^4 raised to the power of 12, we need to simplify each option and compare the results:
Option 1: 3^16
Since the base is the same (3), we add the exponents when we raise a power to another power: 4 * 12 = 48. So, this option is equivalent to 3^48.
Option 2: 3^48
This option is equivalent to 3^48.
Option 3: (3^12)^4
Using the power of a power rule, we multiply the exponents: 12 * 4 = 48. So, this option is equivalent to 3^48.
Option 4: (3^6)^8
Using the power of a power rule, we multiply the exponents: 6 * 8 = 48. So, this option is equivalent to 3^48.
Therefore, none of the options are NOT equivalent to 3^4 raised to the power of 12.
Part b:
To find which expression is NOT equivalent to 3^4 multiplied by 3^6, we need to simplify each option and compare the results:
Option 1: 3^10
Since the bases are the same (3), we add the exponents when we multiply two powers with the same base: 4 + 6 = 10. So, this option is equivalent to 3^10.
Option 2: 9^10
This option is NOT equivalent to 3^4 multiplied by 3^6. 9^10 is equal to (3^2)^10, which is equal to 3^(2*10) = 3^20.
Option 3: (3^5)(3^5)
Using the product of powers rule, we add the exponents: 5 + 5 = 10. So, this option is equivalent to 3^10.
Option 4: (3^2)(3^8)
Using the product of powers rule, we add the exponents: 2 + 8 = 10. So, this option is equivalent to 3^10.
Therefore, the expression NOT equivalent to 3^4 multiplied by 3^6 is 9^10.
are you very sure of your answers?
Upon reviewing my answers again, I realized that I made a mistake in my response. I apologize for the incorrect information provided. Here are the revised answers:
Part a:
The expression 3^4 raised to the power of 12 is equivalent to (3^4)^12, which means we need to multiply the exponents: 4 * 12 = 48.
Now let's compare the given options:
Option 1: 3^16 - This option is not equivalent to (3^4)^12 because the exponent is different. Therefore, the answer is 3^16.
Option 2: 3^48 - This option is equivalent to (3^4)^12 because the exponent is the same. Therefore, it is equivalent.
Option 3: (3^12)^4 - This option is equivalent to (3^4)^12 because the exponent is the same. Therefore, it is equivalent.
Option 4: (3^6)^8 - This option is equivalent to (3^4)^12 because the exponent is the same. Therefore, it is equivalent.
Therefore, the answer is Option 1: 3^16.
Part b:
To find which expression is NOT equivalent to 3^4 multiplied by 3^6, we need to simplify each option and compare the results:
The expression 3^4 multiplied by 3^6 is equivalent to 3^(4+6) = 3^10.
Now let's compare the given options:
Option 1: 3^10 - This option is equivalent to 3^4 multiplied by 3^6. Therefore, it is equivalent.
Option 2: 9^10 - This option is NOT equivalent to 3^4 multiplied by 3^6. It is equivalent to (3^2)^10 = 3^(2*10) = 3^20.
Option 3: (3^5)(3^5) - This option is equivalent to 3^10, which is equivalent to 3^4 multiplied by 3^6. Therefore, it is equivalent.
Option 4: (3^2)(3^8) - This option is equivalent to 3^(2+8) = 3^10, which is equivalent to 3^4 multiplied by 3^6. Therefore, it is equivalent.
Therefore, the answer is Option 2: 9^10.
I apologize for any confusion caused by the initial incorrect answers. Thank you for bringing it to my attention.