Problem 5 - Algebra and Trigonometry

Question

Evaluate each exponential expression. $$ -2^{6} $$

Step-by-Step Solution

Answer

The result of evaluating the exponential expression \( -2^{6} \) is \(64\).

Step 1: Understand Exponential Notation

Exponential notation is a way of representing numbers or expressions in the form \( a^{n} \). Here, 'a' is known as the base and 'n' as the exponent (or power). It represents the operation of multiplying 'a' by itself 'n' times. it doesn't involve making any calculations regarding the base itself but rather what number of times it should be multiplied with itself.

Step 2: Apply Exponential Notation

Apply exponential notation to the given expression \( -2^{6} \). This means that we need to multiply \(-2\) by itself \(6\) times.

Step 3: Calculation

Perform the calculation \((-2) * (-2) * (-2) * (-2) * (-2) * (-2)\) which equals \(64\) since a negative number multiplied by itself an even number of times gives a positive result.