Solving Math Problems With Exponents

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Generally, the base as well as the exponent can be any number (real or complex) or they can even be a variable, unknown factor or parameter.

The equations with the unknown factor is in the exponent are known as exponential equations.

We have the multiplication of powers in the numerator, but we can't resolve it because there are different bases (2 and 3).

In the denominator we have a power with a base of 6 (3·2).

Note: if you have tried to multiply the two numbers shown above, you know that most calculators are not accurate when computing numbers beyond 8 or 10 digits (the numbers are automatically rounded by the calculator).

However, you can Although most people may not stop to think about it, exponents impact most routine financial transactions, either directly or indirectly.Solution: If one side of the square-shaped room is 12 feet, then the area of the room is (12 feet)Summary: To help us remember the order of operations, we can use the mnemonic PEMDAS, which stands for: Please Excuse My Dear Aunt Sally Parentheses, Exponents, Multiplication & Division, Addition & Subtraction Note that although there are six words, they correspond to four rules.Directions: Complete each exercise by applying the rules for order of operations.Rule 4: Perform all additions and subtractions, working from left to right.We can solve the problem above using our revised order of operations.If n is a negative number (-1, -2, -3, -4,...), the result is 0.00...1 where the value of n in positive indicates the number of 0's counting the 0 before the comma.These are the type of powers used in scientific notation.We remember that the symbol ":" is a division, the same way as "/" is.Before we dive into simplifying exponents, let's take some time to learn exactly what an exponent is.We have to clearly identify the factors of the multiplication to apply the rules without making mistakes. We eliminate the first exponent, -1, which means writing the inverse of the base.We also have different bases, but we already know how to solve this problem: writing the bases as products of prime factors and regrouping in powers.