- In the example "2 ^ 3," the "2" is the base and the "3" is the exponent. The base is the number that is multiplied by itself and the exponent is the number that indicates how many times that base number is multiplied, by itself. An exponential expression is a more efficient way to represent the repetitive multiplication. For instance, it is easier to work with "2 ^ 5" than the equivalent multiplication of "2 * 2 * 2 * 2 * 2."
- When one exponential expression is divided by another, the exponents are simplified through subtraction. The division is typically arranged as a fraction, such as "2 ^ 3 / 2 ^ 2." According to the quotient rule, the denominator (bottom) exponent is subtracted from the numerator (top) exponent. In this example, the exponent "2" is subtracted from the exponent "3." The exponent "1" is left, the denominator is eliminated and the expression becomes "2 ^ 1." The expression "2 ^ 1" is simplified further and the final result of the division is "2."
- In algebra, an exponential expression often contains a variable and coefficient in the base, which makes it a "term." In the example "4x ^ 3," the "4" is the coefficient, the "x" is the variable and the "3" is the exponent. For two exponential terms to be divided, both terms have to contain "like" bases. This means that the variables within each base have to be the same. For example, "4x ^ 3" can be divided by "2x ^ 2," but it can't be divided by "2y ^ 5."
- In the example "4x ^ 3 / 2x ^ 2," the terms can be divided because they have like bases (both are "x"). First, the exponent "2" is subtracted from the exponent "3." The result of the subtraction is the exponent "1", and the terms become "4x ^ 1 / 2x." Next, the term "4x ^ 1" is divided by "2x," which eliminates the denominator and results in the single term "2x ^ 1." Finally, "2x ^ 1" is simplified and the overall result of the division is "2x."
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