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 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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  • 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 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 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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  • 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 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 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 is function notation?

    Q: What is function notation?

    A: Function notation is a method of writing algebraic variables as functions of other variables. Most often, functions are portrayed as a set of x/y coordinates, with the vertical y-axis serving as a function of x. For example, writing "f(x) = 3x" is the same as writing "y = 3x."
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  • How do you calculate the pre-exponential factor?

    Q: How do you calculate the pre-exponential factor?

    A: The pre-exponential factor, or frequency factor, is an aspect of the Arrhenius equation and is related to collision theory. The value for this factor varies depending on the chemical reaction and is determined through experimental observation. However, if values of the rate constant, k, are known at different temperatures, an Arrhenius plot is used to determine the pre-exponential factor, A.
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  • Q: What is three squared?

    A: Three squared is nine. The square of a number is obtained by multiplying the number with itself. Thus, the square of three is written as 3^2 or 3 x 3 = 9.
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  • Q: What is the square root of one?

    A: The square root of 1 is 1, just as the square of 1 is 1. The square root of a number finds a result that, when multiplied by itself, equals the original number.
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  • How do you cube a binomial?

    Q: How do you cube a binomial?

    A: Cube a binomial by writing it three times and multiplying each term by using an extrapolated FOIL method. In other words, multiply first terms, outside terms, inside terms, and last terms before combining like terms to achieve the final result.
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  • Q: What is the square root of 10,000?

    A: The square root of 10,000 is 100. The number 10,000 is a perfect square, so it is easy to calculate the square root using the prime factorization method. This is done by listing all the factors of 10,000.
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  • Q: What is the square root of 51?

    A: The square root of 51 is approximately 7.1414284285. There is no precise answer because the square root of 51 is an irrational number, meaning the sequence of numbers after the decimal point never ends and never falls into a repeating pattern.
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  • What are some tricks for calculating square roots?

    Q: What are some tricks for calculating square roots?

    A: To estimate a square root without a calculator, determine the two perfect squares that come before and after the given number. Then using the square roots of the perfect squares as guides, estimate the given number’s square root based on its placement between the two perfect squares.
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  • Q: What is the square root of 20?

    A: The square root of 20 is either 4.47, rounded to the nearest hundredth, or 2 times the square root of 5. The decimal answer is 4.47, and 2 times the square root of 5 is a more precise answer.
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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 a rational exponent?

    A: A rational exponent is an exponent written as a fraction, such as 31/2, which is also equal to the square root of three. With a rational exponent, the numerator indicates the power that the base number is raised to and the denominator indicates the root.
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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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