Evaluate each exponential expression in Exercises 1–22. −2⁶

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Identify the expression given: $-2^6$. Notice that the exponent applies only to the base 2, not to the negative sign, because there are no parentheses around the -2.

Recall the order of operations: exponents are evaluated before multiplication or applying the negative sign. So first, calculate \$2^6$.

Calculate \$2^6$ by multiplying 2 by itself 6 times: $2 \times 2 \times 2 \times 2 \times 2 \times 2$.

After finding the value of \$2^6$, apply the negative sign in front of the result, which means multiply the result by -1.

Write the final expression as $- (2^6)$ and simplify to get the value of the original expression.

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Order of Operations

The order of operations dictates the sequence in which mathematical operations are performed. Exponents are evaluated before multiplication or negation. In the expression −2^6, the exponent applies only to 2, and the negative sign is applied afterward.

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Performing Row Operations on Matrices

Exponents

Exponents represent repeated multiplication of a base number. For example, 2^6 means multiplying 2 by itself six times (2 × 2 × 2 × 2 × 2 × 2). Understanding how to compute powers is essential for evaluating exponential expressions.

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Rational Exponents

Negative Sign and Exponents

A negative sign in front of a base with an exponent can change the result depending on parentheses. Without parentheses, −2^6 means the negative of 2^6, resulting in −64. With parentheses, (−2)^6 means raising −2 to the sixth power, resulting in a positive value.

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