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#Negative exponent rule reciprocal how to

We should remember the following points when using negative exponents.

Use the rule: a m × a n = a (m+n) to combine the common base (7).

Use the rule: (ab) n = a n × b n and split the required number (21).

Convert the negative exponents to positive by writing the reciprocal of the particular number:73×2123473×21234.

Solving negative exponents also involves simplifying terms with negative exponents and applying the given arithmetic operations.Īfter converting all the negative exponents to positive exponents, we simplify Solving equations or expressions requires operating on them.

We should start by writing the expression in its reciprocal form, which makes the negative exponent positive: (5/4)3×(3/10)2.

#Negative exponent rule reciprocal how to

The following example shows how to multiply negative exponents. Using the same rules we use to multiply positive exponents, we multiply negative exponents. After they are converted to fractions, negative exponents become easy to solve because they can be expressed as fractions. Multiplying negative exponents is the same as multiplying any other number. When the sign of an exponent changes, negative exponents become fractions. To see how fractions change from negative exponents, let’s take another example.Ģ -1 can be written as 1/2 and 4 -2 is written as 1/4 2. A negative exponent changes fractions to numbers. With a negative exponent, we get the inverse of the number.

Use the second rule with a negative exponent in the denominator: 1/a -n =a n.

Use the negative exponent rule a -n=1/a n.

Let’s apply these rules to numbers and see how they work. Rule 2: The rule for a negative exponent in the denominator suggests that for each number ‘a’ in the denominator and its negative exponent -n, the result can be written as: 1/a (-n)=a n=a×a×….n times.Rule 1: The negative exponent rule states that for each number ‘a’ with the negative exponent -n, take the reciprocal of the base and multiply it according to the value of the exponent: a (-n)=1/a n=1/a×1/a×….n times.The following are the basic rules for solving negative exponents. The process of simplification is made easier by a set of rules or laws for negative exponents. Negative exponent rule: To turn a negative exponent into a positive one, flip it into a reciprocal.Zero power rule: Increase any base to the power of 0 to make it one.Power of a quotient rule: Assign power to each base when multiplying several variables.Power of a product rule: Distribute power to each base when multiplying several variables.Power of powers rule: Multiply powers together when raising a power by another exponent.

Quotient of powers rule: When dividing like bases, subtract powers.Product of powers: Multiply powers together when multiplying like bases.

The seven laws of exponents are summarized here if you need a refresher: Negative exponents follow the same rules as everything else in math class. See how the number is written in its reciprocal form and how the sign of the powers changes in the table. Here are some examples of negative exponents with variables and numbers. Numbers and Expressions with Negative Exponents Count the 8 -2, here, the base is 8 and we have a negative exponent (-2). We know the reciprocal of the base is multiplied by a negative exponent when we have a negative exponent. For instance, consider 8 2, 8 is the base, and 2 is the exponent. Numbers and Expressions with Negative ExponentsĮxponents indicate how many times you should multiply a base number.