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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  • 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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  • 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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  • 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 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 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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  • 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 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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  • 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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  • 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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  • Q: What Is the Square Root of 34?

    A: Rounded to two decimal places, the square root of 34 is 5.83. It is not possible to simplify the radical ?34 because the number 34 does not have any perfect square factors.
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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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  • Q: How to Graph Exponential Functions?

    A: To graph exponential functions, create a table of values first, calculating the values for f(x) according to the function given. Each pair of numbers constitutes the coordinates for the points to be drawn on the graph. X will give a coordinate for the x-axis, and f(x) is the coordinate for the y-axis.
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  • Q: What Is the Square Root of 72?

    A: The square root of 72 is approximately 8.49 when rounded to the nearest hundredth. Since it is not a perfect square, it can most easily be solved by using a scientific calculator. If this option is unavailable, there are a few tricks you can do to arrive at a solution.
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  • Q: What Is 10 to the Sixth Power?

    A: The number 10 raised to the sixth power is 1,000,000 (one million). When the number 10 is raised to any power, the result will be a number with a one in front of a number of zeros that is equal to the exponent. For example, in this case the answer has six zeros, the same as the power 10 was raised to.
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  • Q: What Is the Square Root of 9?

    A: The square root of the number 9 is 3. That is worked out by deducing that 3 multiplied by 3, or 3 squared, is 9, so the square root is 3.
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  • What Is a Method for Multiplying Fractions With Exponents?

    Q: What Is a Method for Multiplying Fractions With Exponents?

    A: A good method for multiplying fractions with exponents is to factor, cancel and simplify. This works whether the exponent is attached to a variable or a numeral.
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  • Q: What Is the Cube Root of 512?

    A: The cube root of 512 is eight. This is because when eight is cubed, or multiplied by itself three times (8 x 8 x 8), it is equal to 512.
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  • Q: What Is the Significance of Compressibility Factor?

    A: Compressibility factor is significant because it determines how far a gas is from it's ideal state, based on various factors. The compressibility factor is determined by the pressure, volume, temperature and number of moles in the gas.
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  • How Do You Extract Square Roots?

    Q: How Do You Extract Square Roots?

    A: A method of solving quadratic equations is to extract the roots. This means that the possible values of x are determined by finding the square root of both sides of the equation.
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  • Q: What Is the Square Root of 29?

    A: To two decimal places, the square roots of 29 are 5.39 and -5.39. Multiplying either of these roots by itself equals 29, therefore satisfying the definition of a square root.
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  • What Is the Sum of Squared Deviations?

    Q: What Is the Sum of Squared Deviations?

    A: In statistics, the sum of squared deviations refers to how much a set of sample numbers vary or disperse from a given number, usually the mean of the set. When analyzing data, it is important to look at overall variability and the degree of consistency the received scores have.
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