which expression is not equal to the Expression shown below?
3 to the power of 3 divided 3 to the power of -4
responses
A. 3 to the power of 7 divided 3 to the power of 0
B. 3 to the power of -3 divided 3 to the power of 4
C. 3 times 3 to the power of 6
D. 3 to the power of 3 x 3 to the power of 4
The expression that is not equal to the given expression is:
C. 3 times 3 to the power of 6
To determine which expression is not equal to 3 to the power of 3 divided by 3 to the power of -4, we need to simplify each of the given expressions and see if any of them are equal to the original expression.
The original expression is:
3^3 / 3^-4
To simplify this, we can use the rule that when dividing with the same base, we subtract the exponents. So we have:
3^3 / 3^-4 = 3^(3 - (-4)) = 3^7
Now let's simplify each of the given expressions:
A. 3^7 / 3^0 = 3^7 / 1 = 3^7
B. 3^-3 / 3^4 = 1/3^3 / 3^4 = 1/3^(3 + 4) = 1/3^7
C. 3 * 3^6 = 3^1 * 3^6 = 3^(1 + 6) = 3^7
D. 3^3 * 3^4 = 3^(3 + 4) = 3^7
Comparing the simplified expressions to the original expression, we can see that all of the options are equal to the original expression:
A. 3^7 = 3^7
B. 1/3^7 = 1/3^7
C. 3^7 = 3^7
D. 3^7 = 3^7
Therefore, there is no expression among the given options that is not equal to the original expression.