Exponents

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Exponential math is any mathematical operation involving an exponent, which is the number or symbol placed above and after another number or symbol to indicate the power to which the former number is to be raised, Wikipedia explains. The operation 4 x 4, for example, is written exponentially as 4^2.

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  • What Is the Definition of "exponent" in Math?

    Q: What Is the Definition of "exponent" in Math?

    A: In math, the definition of an exponent is a numerical notation that indicates the number of times a number is to be multiplied by itself. The exponent is written as a small number in superscript following the number to be multiplied.
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  • What Method Is Used for Dividing Negative Exponents?

    Q: What Method Is Used for Dividing Negative Exponents?

    A: Because a negative exponent turns the base into its reciprocal, a simple method for dividing negative exponents is letting the negative cancel and multiplying by the positive exponential expression. Regents Prep notes that when multiple exponents have the same base, the terms can be easily divided or multiplied because the exponents themselves can be added or subtracted.
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  • What Are Logs and Exponents?

    Q: What Are Logs and Exponents?

    A: Exponents are numbers that indicate the number of times a function is multiplied by itself, while logs are used to determine the exponential function needed to express a particular number or mathematical phrase. Exponents can be expressed through log functions, and logs can be expressed through exponential functions.
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  • What Are the Division Properties of Exponents?

    Q: What Are the Division Properties of Exponents?

    A: The division properties of exponents are: when dealing with like bases, exponents are subtracted when the bases are divided; when an entire quotient is raised to an exponential power, both the numerator and denominator are raised to the power before division is performed. One way to employ the division properties of exponents is to expand the terms above and below the dividing line for like bases.
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  • What Is a List of Perfect Squares?

    Q: What Is a List of Perfect Squares?

    A: A list of perfect squares under 100 includes 1, 4, 9, 16, 25, 36, 49, 64 and 81. Perfect squares are infinite in number because they are found by multiplying a number by itself, meaning that the possibilities are endless. Although there are many square numbers, perfect squares are unique and very easy to calculate since whole numbers are involved.
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  • Who Invented Exponents?

    Q: Who Invented Exponents?

    A: Euclid discovered the concept underlying the exponent, calling the area of a square a power of the length of a single side. Archimedes later generalized the idea of powers in his work, "The Sand Reckoner." He discovered and proved the law of exponents in the same work.
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  • What Is an Exponent in Standard Form?

    Q: What Is an Exponent in Standard Form?

    A: The standard form of an exponent is how people see numbers normally. For example, five to the sixth power is in exponent form, and the standard form of this exponent is 15,625.
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  • How Is "exponential Math" Defined?

    Q: How Is "exponential Math" Defined?

    A: Exponential math is any mathematical operation involving an exponent, which is the number or symbol placed above and after another number or symbol to indicate the power to which the former number is to be raised, Wikipedia explains. The operation 4 x 4, for example, is written exponentially as 4^2.
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  • In What Real-Life Situations Would You Use Polynomials?

    Q: In What Real-Life Situations Would You Use Polynomials?

    A: Polynomials are often used to find the displacement of an object under the influence of gravity. They can also be used in real-life situations from financial planning to meteorology.
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  • Q: What Is the Prime Factorization of 49?

    A: The prime factorization of 49 is equal to 7*7. The prime factorization of a number is a way of representing a number as the result of two or more prime factors.
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  • Q: What Is the Square Root of 121?

    A: The square root of 121 is 11 or negative 11. The factors of 121 are 11 x 11. Similarly, negative 11 x negative 11 is also 121. To obtain an exact square root, the number must be a perfect square.
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  • Q: What Is the Square Root of 28?

    A: The square root of 28 is 5.29, rounded to two decimal places, as 28 is not a perfect square. The square root of a perfect square is a whole number and not a decimal or fraction. The square root of 25 is 5, as 25 is a perfect square.
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  • Q: What Are the Steps in Multiplying Polynomials With Exponents?

    A: The steps for multiplying polynomials with exponents vary depending on the complexity of the polynomials. If the equation has only one variable, the answer can be found by multiplying the individual terms, combining the terms with the same degree and simplifying.
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  • Q: What Are Some Basic Operations With Polynomials?

    A: The four basic operations of polynomials are addition, subtraction, multiplication and division. Polynomials are algebraic expressions that contain one or more variables. The coefficient of the polynomial is the number that is written in front of the variable.
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  • What Is the Inverse of an Exponential Function?

    Q: What Is the Inverse of an Exponential Function?

    A: The inverse of an exponential function is a logarithm function. An exponential function written as f(x) = 4^x is read as "four to the x power." Its inverse logarithm function is written as f^-1(y) = log4y and read as "logarithm y to the base four."
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  • Q: What Is the Square Root of 125?

    A: The square root of 125 is approximately 11.18. The decimals of the exact answer go on infinitely because the square root of 125 is an irrational number.
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  • Q: What Is the Square Root of 36?

    A: The square roots of 36 are 6 and -6. The square root of a number is a number that, when multiplied by itself, results in the original number. A number that is the square of a whole number, such as 36, is called a perfect square.
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  • Q: What Is the Square Root of 4000?

    A: The square root of 4,000 is 63.24. That value can be obtained by using the radical function on either a scientific or graphing calculator. The square root of 4,000 can also be written as 20 times the square root of 10.
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  • How Do You Convert From Log to Exponential Form?

    Q: How Do You Convert From Log to Exponential Form?

    A: Converting logarithms to exponential form is a matter of knowing which symbols represent which part of the equation and directly substituting. This conversion can be done in under a minute, and a calculator is only useful if you want to check your answer.
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  • What Are Some Multiples of 3?

    Q: What Are Some Multiples of 3?

    A: Some multiples of 3 are 6, 9, 12, 21, 300, -3 and -15. All numbers that are equal to 3 multiplied by an integer (a whole number) are multiples of 3.
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  • Q: What Is an Example of a Whole Number That Equals 25 When It Is Squared and 125 When It Is Cubed?

    A: The number 5 is a whole number that equals 25 when it is squared and 125 when it is cubed. Five is the only number, whole or otherwise, that satisfies both of these criteria.
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