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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  • 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 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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  • 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 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 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 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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  • Q: What is 4 squared in math?

    A: Four squared in math is 16, as any number squared is multiplied by itself. Another way to express four squared is to say four to the second power.
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  • What are the factors of 100?

    Q: What are the factors of 100?

    A: The factors of 100 are 2, 2, 5 and 5. To find the prime factorization of a number, the number is divided by prime numbers that go evenly into the original value until only one prime number is left. For example, 100 divided by 2 is 50, and then 50 divided by 2 is 25, and then 25 divided by 5 is 5, giving the prime factorization of 2 x 2 x 5 x 5.
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  • Q: How do you find a number's square root?

    A: Find the square root by finding the number that, when multiplied by itself, gives you the root number. For root numbers that are not perfect squares, there is a separate process to finding the square root.
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  • Q: How do you find square roots?

    A: To calculate the square root of any number, estimate by using the closest perfect square, and divide the number for which you want the square root by the root of that perfect square. Average the result with that perfect square root, repeating the process as you approach the closest number possible.
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  • Q: What is the cube root of 250?

    A: The cube root of 250 is 6.29. The cube root of a number, x, is equal to the number, y, such that y times y times y equals x. For the number 250, 6.29 times 6.29 times 6.29 is equal to 250.
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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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  • 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 Maclaurin series for ln(1+x)?

    A: The Maclaurin series for ln(1+x) is ln(1+x) = x - x^2/2 + x^3/3 - x^4/4 + x. This series gives an approximate value of ln(1+x) when x is between minus one and one. The more terms are included, the more accurate the value will be.
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  • How do you solve equations with PEMDAS?

    Q: How do you solve equations with PEMDAS?

    A: PEMDAS, or Please Excuse My Dear Aunt Sally, is the mnemonic device for order of mathematical operations used to solve algebraic equations. It represents parentheses, exponents, multiplication, division, addition and subtraction. Equations cannot just be solved left-to-right because the proper order of operations must be observed.
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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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  • What is the exponential parent function?

    Q: What is the exponential parent function?

    A: The exponential parent function is the most basic form of an exponential function. From the general form of an exponential function y = ab^x, an exponential parent function has a value for a equal to one. Therefore, the exponential parent function is written simply as y = b^x.
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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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