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The negative exponents describe how many times we have to divide the base number. Visit BYJU’S to learn the definition, rules, procedure for solving the negative exponents with examples.
This quick lesson explains the negative exponent rule in 3 easy steps and includes a visual animation to help you better understand the negative exponent rule.
A negative exponent is defined as the reciprocal (or multiplicative inverse) of the base, raised to the corresponding positive exponent. Thus, while positive exponents involve repeated multiplication of a number, negative exponents indicate how many times to divide by that number.
What is the Rule for Negative Exponents? There are two main rules that are helpful when dealing with negative exponents: a-n = 1/a n; 1/a-n = a n; How to Solve Fractions with Negative Exponents? Fractions with negative exponents can be solved by taking the reciprocal of the fraction.
For any non zero real number a and any integer n, the negative exponent rule is the following \(a^{−n}= \dfrac{1 }{a^n} or \dfrac{1 }{a^{−n}} = a^n\) It is poor form in mathematics to leave negative exponents in the answer.
A negative exponent means how many times to divide by the number. Example: 8-1 = 1 ÷ 8 = 1/8 = 0.125. Or many divides: Example: 5-3 = 1 ÷ 5 ÷ 5 ÷ 5 = 0.008. But that can be done an easier way: 5-3 could also be calculated like: 1 ÷ (5 × 5 × 5) = 1/53 = 1/125 = 0.008. That last example showed an easier way to handle negative exponents:
The Product Rule for Exponents states that x m • x n = x m+n. "When multiplying exponential expressions, if the bases are the same, add the exponents." If we apply this law to work with a negative exponent, we get 4 3 • 4 -3 = 4 3+(-3) = 4 0 = 1.
Negative exponent rule: To convert a negative exponent to a positive one, write the number into a reciprocal. How to Solve Negative Exponents? 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.
Simplify the expression \[\dfrac{x^{-3}y^2}{3z^{-4}} \nonumber \]so that the resulting equivalent expression contains no negative exponents. Answer \(\dfrac{y^2z^4}{3x^3}\)
Negative exponents. A negative exponent is equal to the reciprocal of the base of the negative exponent raised to the positive power. This is expressed as. where b is the base, and n is the power.