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

5
5

403
Start Fraction 40 over 3 End Fraction

193+4/3(10−7⋅4)

Answer 1

Let's evaluate the original expression step-by-step:

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

1. Evaluate \( 193^0 \):

   • Any number raised to the power of 0 is 1, so \( 193^0 = 1 \).

2. Evaluate \( 4^0 \):

   • Similarly, \( 4^0 = 1 \).

3. Substituting values into the expression:

   • Replace \( 193^0 \) and \( 4^0 \): \[ 1 + \frac{4}{3}(10 - 7 \cdot 1) \]
   • This simplifies to: \[ 1 + \frac{4}{3}(10 - 7) = 1 + \frac{4}{3}(3) \]

4. Simplify further:

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

So the expression evaluates to \( 5 \).

Now let's check which of the response options is equal to \( 5 \):

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

  • This simplifies to \( 193 + \frac{4}{3}(3) = 193 + 4 = 197 \).

• Option 2: \( 5 \)

  • This equals \( 5 \).

• Option 3: \( \frac{40}{3} \)

  • This equals \( \approx 13.33 \).

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

  • This simplifies as follows:
  • \( 10 - 28 = -18 \):
  • \( 193 + \frac{4}{3}(-18) = 193 - 24 = 169 \).

The correct answer is:

5