which of the dollowing is an equivalent expression to 7/(-5.3)^0 + 4.9 when applying the zero power rule?

Question

A. 7/5.3^0 + 36
B. 7/0 + 4.9
C. 7/5.3 + 4.9
D. 7/1 + 4.9

Answer 1

To solve this, we first need to apply the zero power rule. The zero power rule states that any non-zero number raised to the power of zero is equal to one.

In the expression \(7/(-5.3)^0 + 4.9\):

1. \((-5.3)^0 = 1\) (because any non-zero number to the power of 0 is 1).
2. Thus, \(7/(-5.3)^0\) becomes \(7/1\).
3. So, the expression simplifies to \(7/1 + 4.9\), which is \(7 + 4.9\).

Now, looking at the answer choices:

A. \(7/5.3^0 + 36\) (not equivalent) B. \(7/0 + 4.9\) (not equivalent; division by zero) C. \(7/5.3 + 4.9\) (not equivalent) D. \(7/1 + 4.9\) (this is equivalent)

Thus, the correct answer is:

D. 7/1 + 4.9