Solving Exponential Problems

Solving Exponential Problems-42
Thus, we are now able to handle any integer exponents, whether positive or negative.

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

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Conversion to standard form simply requires movement of the decimal point the number of places indicated by the exponent.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.o Scientific notation Objectives o Derive the rules for multiplying and dividing exponential expressions o Determine the meaning of a negative exponent o Apply exponents to understanding and using scientific notation Exponents are a way of representing repeated multiplication (similarly to the way multiplication is a way of expressing repeated addition).In some instances, we may need to perform operations on numbers with exponents; by learning some basic rules, we can make the process much simpler.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.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.We can see that the exponent of the answer is the difference between that of the numerator and that of the denominator (again, all have the same base).Let's generalize the rule: Notice that the expression in parentheses has three factors, and we must multiply this expression four times.

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