Simplify each of the following quotients as much as possible using the power of a quotient rule. ![]() In case both the bases and the exponents are different we calculate each exponent separately and then multiply:ģ -2 x 4 -3 = (1/9) x (1/64) = 1 / 576 = 0.\): Using the Power of a Quotient Rule In other words, 1 is divide by the reciprocal of the base raised to a positive exponent of 2 The base 2/3 raised to the negative exponent of 2 is equal to 1 divided by the base 2/3 raised to the positive exponent of 2. The rule implies that, if a fraction a/b is raised to the negative exponent of n, it is equal to 1 divided by the base a/b raised to the positive exponent of n: You should notice that a fractional negative exponent is the same as finding the root of the base. It implies that, if the base 2 is raised to the negative exponent of 1/2, it is equivalent to 1 divided by the base 2 raised to the positive exponent of 1/2: The base b raised to the negative power of n/m is equivalent to 1 divided by the base b raised to the positive exponent of n/m: The general formula of this rule is: a -m = 1/a m and (a/b) -n = (b/a) n.īelow are examples of how negative exponent rule works: The law of negative exponents states that, when a number is raised to a negative exponent, we divide 1 by the base raised to a positive exponent. Negative exponent rule: To convert a negative exponent to a positive one, write the number into a reciprocal.Zero power rule: This rule implies that, any base raised to a power of zero is equal to one.Power of a quotient rule: Distribute power to each base when raising several variables by a power.Power of a product rule: Distribute power to each base when raising several variables by a power.Power of powers rule: Multiply powers together when raising a power by another exponent.The rule about multiplying exponents when the bases are the same is to add the. Quotient of powers rule: When dividing like bases, the powers are subtracted Every non-negative number Rational Exponents The numerator of a.Multiplication of powers with same base: With multiplication of like bases, add the powers together.How to solve Fractions with negative exponentsīefore we tackle each one of these topics, let us do a quick recap of the rules of exponents.To help you understand the negative exponent rule better, this paper discusses in detail the following topics of negative exponent rule: If you are wondering where to begin, don’t worry, this article is going to help you transform your course on negative exponents into a positive experience. This is because, it equips students with the necessary skills and knowledge to face challenging problems in and out of the classroom. Learning negative exponents is a major foundation block for solving advanced mathematical expressions. It normally a total disaster when negative exponents are added to the equations. Many students will find it hard to understand negative numbers and fractions. They are widely used in algebraic problems, and for this reason, it is important to learn them so as to make the studying algebra easy. For example, 3 x 3 x 3 x 3 can be written in exponential form as 3 4 where 3 is the base and 4 is the exponent. The general form of an exponential expression is b n. An exponential expression consists of two parts, namely the base, denoted as b and the exponent, denoted as n. Negative Exponents – Explanation & ExamplesĮxponents are powers or indices.
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