New SAT Math Exponents and Exponential Expressions

Exponents on the New SAT will test you on your mastery of the basic rules you probably have already learned in math class. The concepts arent hard to understand, but it can seem nearly impossible to recall if you havent been exposed to them recently. New SAT test makers will do their best to try to make you fumble your way through an exponents problem by scaring you with seemingly challenging problems. However, once you have the basics down, theres not much they can do to trick you or cause a silly mistake. You might be thinking that you can just plug and chug on problems your calculator, but in many cases, simplifying exponents is a lot faster by hand. Furthermore, some problems are impossible to do with a calculator because of the sheer size of the values you need to calculate. Lastly, you may bump into exponent problems on the non-calculator section, but never fear! Heres how to tackle them. New SAT Math: Exponent Rules Multiplying Exponents When you multiply two terms that have a base with the same value, add the exponents together to get to your answer. The base value stays the same. Dividing Exponents In contrast, when you divide two terms that have a base with the same value, subtract the exponents to get to your answer. The base value stays the same here as well. Raising Exponents to a Power When raising an exponent to a power, multiply the exponents together. Raising Products to a Power When raising products to a power, each factor is raised to that power. New SAT Math: Special Exponents Exponents to the Power of 0 Anything raised to the power of 0 gives you a value of 1. Negative Exponents When you have negative exponent, all you have to do is take the reciprocal of it and rewrite it with a positive exponent. In other words, flip the exponent onto the other side of the fraction line. Fractional Exponents The numerator of the exponent tells you the power of the exponent. The denominator of the exponent tells you the index of the radical. In other words, its a two-step problem. You need to raise the term to a certain power, and then take the root of it. New SAT Math: Simplifying Exponential Expressions Not these kinds of expressions! You will encounter questions that ask you to simplify exponential expressions. To make the expressions tougher to solve, theyll usually be multi-step problems involving special exponents and fractions. When doing problems that have to deal with exponents, stick to the basics. Keep your order of operations in mind, and be careful not to invent math rules that dont exist. With a bit of practice, these problems will be a snap for you to overcome on test day! For more New SAT Math concepts, check out our posts on quadratic equations and how to answer graph and chart questions.