Which of the following expressions is equal to 193^0+4/3(10−7⋅4^0)

Question

?(1 point)
Responses

193+43(10−7⋅1)
193 plus Start Fraction 4 over 3 End Fraction left parenthesis 10 minus 7 times 1 right parenthesis

193+43(10−7⋅4)
193 plus Start Fraction 4 over 3 End Fraction left parenthesis 10 minus 7 times 4 right parenthesis

403
Start Fraction 40 over 3 End Fraction

5

Answer 1

Let's simplify the original expression step by step:

The original expression is:

\[ 193^0 + \frac{4}{3}(10 - 7 \cdot 4^0) \]

1. Evaluate \(193^0\): Any non-zero number raised to the power of 0 is 1, so:

   \[ 193^0 = 1 \]

2. Evaluate \(4^0\): Similarly, \(4^0 = 1\).

3. Substitute back into the expression:

   \[ 1 + \frac{4}{3}(10 - 7 \cdot 1) \] \[ = 1 + \frac{4}{3}(10 - 7) \] \[ = 1 + \frac{4}{3}(3) \] \[ = 1 + \frac{12}{3} \] \[ = 1 + 4 \] \[ = 5 \]

Now let's evaluate the options given:

1. Option 1: \(193 + \frac{4}{3}(10 - 7 \cdot 1)\)

   This simplifies to \(193 + \frac{4}{3}(10 - 7)\), which does not equal 5.

2. Option 2: \(193 + \frac{4}{3}(10 - 7 \cdot 4)\)

   This simplifies to \(193 + \frac{4}{3}(10 - 28)\), which also does not equal 5.

3. Option 3: 403

   This is simply 403, and it does not equal 5.

4. Option 4: \(\frac{40}{3}\)

   This does not equal 5 either.

Since we evaluated the original expression and found it equal to 5, the correct response is:

5