Apply the zero power rule to create an equivalent expression to (-33) to the power of zero + 3/2 (8 minus 27 to the power of 0

1 answer

The zero power rule states that any non-zero number raised to the power of zero equals one. Therefore, we can simplify the expression given:

  1. \((-33)^0 = 1\) (since \(-33\) is non-zero)
  2. \(27^0 = 1\) (since 27 is also non-zero)

Now we can substitute these values into the expression:

\[ (-33)^0 + \frac{3}{2} (8 - 27^0) = 1 + \frac{3}{2} (8 - 1) \]

Next, simplify inside the parentheses:

\[ 8 - 1 = 7 \]

Now substitute that back into the expression:

\[ 1 + \frac{3}{2} \times 7 = 1 + \frac{21}{2} \]

Now, we need to combine the terms:

To add 1 to \(\frac{21}{2}\), we can express 1 as \(\frac{2}{2}\):

\[ 1 = \frac{2}{2} \]

So now we can add:

\[ \frac{2}{2} + \frac{21}{2} = \frac{2 + 21}{2} = \frac{23}{2} \]

Thus, the equivalent expression is:

\[ \frac{23}{2} \]