They can be used to represent very large or very small numbers. They represent the reciprocal of the base raised to the positive exponent. In summary, negative exponents are a shorthand way of writing fractions or decimals. For example, -2 raised to the power of 3 is equal to -8, but (-2) raised to the power of 3 is equal to -8. It is important to note that negative exponents only apply to powers of numbers, not to the numbers themselves. ![]() Similarly, instead of writing 1000000, one can write 10 raised to the power of 6. For instance, instead of writing 0.0001, one can write 10 raised to the power of -4. Negative exponents can be used to represent very large or very small numbers. ![]() This is because 3 raised to -2 is equal to 1 divided by 3 raised to 2. For instance, if 3 is raised to -2, then it is equivalent to 1/3 raised to 2. In general, if a number is raised to a negative exponent, it is the reciprocal of the same number raised to the positive exponent. A negative exponent indicates how many times the base should be divided by itself.įor example, if the exponent is -3 and the base is 2, then 2 raised to the power of -3 is equal to 1 divided by 2 raised to the power of 3. Negative exponents are a way of representing fractions or decimals in a more compact form. Related Topics: Product Rule, Quotient Rule, Power of a Power Rule, Power of a Quotient Rule, Power of a Product Rule While negative exponents may seem intimidating at first, with practice, they can become second nature. It is also essential in scientific notation, where negative exponents are used to represent very small numbers. Understanding negative exponents is crucial for solving complex equations involving variables and exponents. In simple terms, negative exponents represent the inverse of a number raised to a positive exponent. Negative exponents can be a challenging concept to grasp for many students, but they are an essential part of algebra and higher-level math. If there are any other like terms, you must simplify the problem by either multiplying or dividing the exponents of the like terms. If there is nothing left on one side of the fraction line, you use the number one as a place holder. Once the term has been flipped over the fraction line, the exponent becomes positive. ![]() The shortcut for changing negative exponents into positive exponents, is to flip the term with a negative exponent over the fraction line. ![]() In order to simplify bases raised to negative exponents, you must make the exponents positive. For each rule, we’ll give you the name of the rule, a definition of the rule, and a real example of how the rule will be applied.įor all examples below, assume that X and Y are nonzero real numbers and a and b are integers.ĭefinition: Any nonzero real number raised to the power of zero will be 1.ĭefinition: Any nonzero real number raised to a negative power will be one divided by the number raised to the positive power of the same number.ĭefinition: When multiplying two exponents with the same nonzero real number base, the answer will be the sum of the exponents with the same baseĭefinition: When dividing two exponents with the same nonzero real number base, the answer will be the difference of the exponents with the same base.ĭefinition: If an exponent is raised to another exponent, you can multiply the exponents.ĭefinition: If the product of two nonzero real numbers is being raised to an exponent, you can distribute the exponent to each factor and multiply individually.ĭefinition: If the quotient of two nonzero real numbers are being raised to an exponent, you can distribute the exponent to each individual factor and divide individually.Negative Exponents refer to bases that are raised to a power that is negative. What?! Confusing much? In this article, we’ll review 7 KEY Rules for Exponents along with an example of each. Exponents can be a tricky subject to master – all these numbers raised to more numbers divided by other numbers and multiplied by the power of another number.
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