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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  • 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 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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  • 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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  • 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 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 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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  • 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 square root of 3?

    A: The square root of 3 is 1.7320508, or approximately 1.73. The calculation may be quickly performed by hitting the square root symbol followed by 3 on a calculator.
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  • What is the opposite of a square root?

    Q: What is the opposite of a square root?

    A: The opposite of finding the square root of a number is squaring the number. Squaring a number means multiplying the figure by itself. For example, the square root of four is two, and two squared is four.
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  • What are exponents with fractions?

    Q: What are exponents with fractions?

    A: If an exponent is a fraction, such as y^1/n, the correct operation is to take the nth root of the base number y. For example, 27^1/3 is the same thing as taking the cube root of 27, so the answer is 3.
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  • What are negative and fractional exponents?

    Q: What are negative and fractional exponents?

    A: A negative exponent is one preceded by a minus sign, as in 5^(-5), while a fractional exponent is one that is not a whole number, such as 5^(3/5). An exponent can be both negative and a fraction, as in the number 6^(-1/2).
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  • Q: What is the square root of 12?

    A: The square root of 12 is 3.46, rounded to two decimal places. The square root is written as 2 times the square root of 3, in its simplest form. The function may be performed on most calculators by hitting the square root button followed by 12.
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  • Q: What is the square root of 160?

    A: The principal square root of 160 is 12.65 to two decimal places. The other square root of 160 is minus 12.65 to two decimal places. All real numbers have two square roots, one of which is the negative of the other.
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  • Q: How do you solve a problem when you have different bases with the same exponents?

    A: When multiplying or dividing different bases with the same exponent, combine the bases, and keep the exponent the same. For example, X raised to the third power times Y raised to the third power becomes the product of X times Y raised to the third power. When adding or subtracting different bases with the same power, evaluate the exponents first, and then perform the summation.
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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 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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  • What are exponential function rules?

    Q: What are exponential function rules?

    A: Exponential function rules are the mathematical guidelines for functions that take the form of f(x) = b^x, where the base is a positive real number. With these functions, the growth rate is proportional to their value.
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  • What is a rational exponent notation?

    Q: What is a rational exponent notation?

    A: Rational or fractional exponents are another way of notating that some root of a base number should be taken, without using a radical sign. For instance, 16^1/2 is equivalent to taking the square root of 16, and 27^1/3 is equivalent to taking the cube root of 27.
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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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