Solving Exponential Problems

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These rules can be of great value in more advanced algebra when dealing with variables (or otherwise unspecified numbers) that have exponents..

The "brute force" approach to finding the product would be to expand each exponent, multiply the results, and convert back to an exponent (assuming an exponential representation of the result is desired).

Thus, we are now able to handle any integer exponents, whether positive or negative.

We also know how to multiply and divide exponential expressions.

For a negative exponent, the decimal point must be moved to the left, and for a positive exponent, it must be moved to the right.

If something increases at a constant rate, you may have exponential growth on your hands.Note that we can obtain the larger number by repeatedly multiplying 1.37 by 10 some number of times.Scientific notation is this method of representing numbers.Note carefully that when we multiply two exponents (again, assuming they have the same base), the result is multiplication of the factors of the first exponent and the factors of the second exponent.The total number of factors is thus the sum of the two exponents.The general format is a single integer digit followed by some number of decimal places, all multiplied by an integer power of 10.Let's take a look at two more examples of conversion from standard notation to scientific notation.Thus, we can do the following: The simple way to look at this is that any factors in the numerator can simply cancel equivalent factors in the denominator.Thus, for every instance where 2 appears in the numerator and denominator, we can cross that pair off.Later in the course, we will consider fractional exponents.(As it turns out, fractional exponents obey the same rules as integer exponents, but the precise meaning of a fraction will be made clear later on.) Although exponents may at times seem like an obscure or less than practical mathematical tool, they have numerous important and practical applications.


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