Exponent refresher: Evaluate the rule for exponents – any number raised to the power of 1 equals what?

Introduction / Context:
Basic exponent rules are fundamental in electronics, controls, and signal processing. They underpin scientific notation, frequency scaling, and power calculations.

Given Data / Assumptions:

• We consider real numbers a ≠ 0.
• The exponent is exactly 1.
• We apply the standard exponent identity laws.

Concept / Approach:
By definition of exponents and the identity element for multiplication, a^1 = a. This follows from the law a^m * a^n = a^(m+n). Setting m = 0 and n = 1 gives a^0 * a^1 = a^(0+1) = a^1. Since a^0 = 1, we have 1 * a^1 = a, so a^1 = a.

Step-by-Step Solution:
Start from a^m * a^n = a^(m+n).Let m = 0, n = 1: a^0 * a^1 = a^1.Because a^0 = 1, the left side reduces to 1 * a^1.Therefore, a^1 = a (the original number).

Verification / Alternative check:
Test with examples: 10^1 = 10; 2^1 = 2; (-3)^1 = -3. The identity holds universally for real numbers.

Why Other Options Are Wrong:
Zero (option A) would imply all numbers equal zero when exponent is 1, which is false.

One (option B) corresponds to a^0, not a^1.

Two (option C) is arbitrary and incorrect.

Reciprocal (option E) corresponds to a^(-1), not a^1.

Common Pitfalls:
Mixing up a^0 = 1 and a^1 = a; keeping the exponent rules straight avoids algebra errors in engineering derivations.

Final Answer:
that number.