Consider the numerical expression: 3 ^ 4
If the given expression is raised to the power of 12, which expression is NOT equivalent?
A 3 ^ 16
B 3 ^ 48
C (3 ^ 12) ^ 4
D (3 ^ 6) ^ 8
If the given expression is multiplied by 3 ^ 6 which expression is NOT equivalent?
A 3 ^ 10
B 9 ^ 10
C (3 ^ 5)(3 ^ 5)
D (3 ^ 2)(3 ^ 8)
For the first question, to determine which expression is NOT equivalent to 3^4 raised to the 12th power, we can simplify each expression and compare them.
3^4 raised to the power of 12 is equivalent to 3^(4*12) = 3^48.
A. 3^16 is NOT equivalent because 3^16 is less than 3^48.
B. 3^48 is equivalent.
C. (3^12)^4 = 3^(12*4) = 3^48, so it is equivalent.
D. (3^6)^8 = 3^(6*8) = 3^48, so it is equivalent.
Therefore, the expression that is NOT equivalent is A. 3^16.
For the second question, to determine which expression is NOT equivalent to 3^4 multiplied by 3^6, we can simplify each expression and compare them.
3^4 multiplied by 3^6 is equivalent to 3^(4+6) = 3^10.
A. 3^10 is equivalent.
B. 9^10 is equivalent, as 9 = 3^2, so this is equivalent to (3^2)^10 = 3^(2*10) = 3^20.
C. (3^5)(3^5) = 3^(5+5) = 3^10, so it is equivalent.
D. (3^2)(3^8) = 3^(2+8) = 3^10, so it is equivalent.
Therefore, the expression that is NOT equivalent is B. 9^10.