Add parentheses to make the equation 3^2x11-8+16 = 43 true

Answer 1

To make the equation \(3^2 \times 11 - 8 + 16 = 43\) true by adding parentheses, we'll investigate different groupings and operations.

Start with the given equation:
\[3^2 \times 11 - 8 + 16\]

First, evaluate the left-hand side without any parentheses:

\[3^2 = 9\]
\[9 \times 11 = 99\]
\[99 - 8 = 91\]
\[91 + 16 = 107\]

We need to add parentheses so that the expression equals 43. Let's try different groupings of operations:

Option 1:
\[(3^2 \times 11 - 8) + 16\]

Evaluate inside the parentheses first:
\[3^2 = 9\]
\[9 \times 11 = 99\]
\[99 - 8 = 91\]
Then add 16:
\[91 + 16 = 107\]

This doesn't work; it still equals 107.

Option 2:
\[3^2 \times (11 - 8 + 16)\]

Evaluate inside the parentheses first:
\[11 - 8 = 3\]
\[3 + 16 = 19\]
Then multiply by 9 (since \(3^2 = 9\)):
\[9 \times 19 = 171\]

This also doesn't work, as it equals 171.

Option 3:
\[3^{(2 \times 11)} - 8 + 16\]

Evaluate the exponent first:
\[2 \times 11 = 22\]
\[3^{22}\] is an extremely large number, which isn't practical.

Option 4:
\[(3^2 \times 11) - (8 + 16)\]

Evaluate inside the parentheses first:
\[3^2 = 9\]
\[9 \times 11 = 99\]
Then inside the other parentheses:
\[8 + 16 = 24\]
Subtract 24 from 99:
\[99 - 24 = 75\]

This doesn't work either, as the result is 75.

Option 5:
\[3^{(2 \times (11 - 8))} + 16\]

Evaluate inside the inner parentheses first:
\[11 - 8 = 3\]
Then evaluate the exponent:
\[2 \times 3 = 6\]
\[3^6 = 729\]
Then add 16:
\[729 + 16 = 745\]

This sums to 745, which is far from 43.

Let's try a different approach.

Option 6:
\[(3^2 \times (11 - 8)) + 16\]

Evaluate inside the inner parentheses first:
\[11 - 8 = 3\]
Then multiply by 9:
\[3^2 = 9\]
\[9 \times 3 = 27\]
Then add 16:
\[27 + 16 = 43\]

So, the correct placement of parentheses to make the equation true is:
\[(3^2 \times (11 - 8)) + 16 = 43\]

Hence the solution is:
\[ (3^2 \times (11 - 8)) + 16 = 43 \]