Evaluate the exponential expression 8^2 times 3.

Step-by-step solution

1. 1

   Decide what the exponent is attached to. In $8^{2}\cdot 3$ the little $2$ sits on the $8$ alone. There are no brackets around $8\cdot 3$, so the multiplication is not part of the base.

2. 2

   Evaluate the power first. Exponents outrank multiplication in the order of operations:

   $8^{2}=8\cdot 8=64.$

3. 3

   Now multiply.

   $64\cdot 3=192.$

4. 4

   Compare with the misreading. If the expression had been $(8\cdot 3)^{2}$ the answer would be $24^{2}=576$ — three times larger. Deciding the base before computing anything is what keeps these apart.

5. 5

   Check with prime factors. $8^{2}\cdot 3=\left(2^{3}\right)^{2}\cdot 3=2^{6}\cdot 3=64\cdot 3=192$, confirming the value.