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Understanding the concept of the base and exponent is fundamental when working with exponentiation. The 'base' refers to the number that is being multiplied, and the 'exponent' denotes how many times the base is multiplied by itself. For instance, in the expression \(2^{6}\), the number 2 is the base, and 6 is the exponent. This indicates that the number 2 is to be used as the starting figure for multiplication, and this multiplication will occur 6 times over. It's like having six 2s, and you're planning to multiply them all together, one after the other.

It's crucial to note that the exponent is not a multiplier of the base but rather the number of times the base will undergo multiplication.

Repeated multiplication is a way to simplify large calculations by using the same number several times. When you see an expression like \(2^{6}\), you can break it down into simpler steps: start with the base, which is 2, then multiply it by itself, and then continue multiplying the result by the base until you’ve done so six times in total. This means \(2 \times 2 \times 2 \times 2 \times 2 \times 2\), which eventually simplifies down to 64.

This method of calculation is advantageous because it transforms what might seem like a difficult problem into a series of simpler ones. However, always remember to keep track of each multiplication step, as losing count could lead to an inaccurate result.

Numerical value is the definite, quantifiable result you obtain from performing calculations, such as those in exponentiation. When you work out \(2^{6}\), you're ultimately looking to find out what single number this expression corresponds to—its numerical value.

In our case, by repeatedly multiplying the base number—a process we've already described—we find that \(2^{6}\) equals 64, and thus the numerical value is 64. It's important to reach this final number because it represents the outcome of the exponentiation process - a concrete figure that may be used in further calculations or to answer the question at hand.