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 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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  • 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 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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  • 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 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 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 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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  • 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 25?

    A: The square root of the number "25" is either five or negative five. A square root of a given number is the number that when multiplied by itself yields that given number.
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  • Q: What is 6.02 times 10 to the 23rd power?

    A: The equation of 6.02 times 10 to the 23rd power is equal to 602,000,000,000,000,000,000,000, or 602 followed by 21 zeros. This number is read aloud as "602 sextillion" and is a reference to Avogadro's number.
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  • What are the first eight multiples of the number six?

    Q: What are the first eight multiples of the number six?

    A: The first eight multiples of the number six are 6, 12, 18, 24, 30, 36, 42 and 48. Multiples are obtained by multiplying a number by integers, so the multiples of 6 can be obtained by multiplying 6 by integers starting from 1.
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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 10 to the 12th power?

    A: Ten to the 12th power is equal to 10 being multiplied by itself 12 times. Ten to the power of 12 is 1,000,000,000,000, or one trillion.
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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 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 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: What are the laws of exponents in math?

    A: The laws of exponents consist of the power rule, product rule, quotient rule, zero rule, rules of one and rules of negative exponents. These tools prove useful for simplifying and manipulating mathematical expressions with exponents.
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  • Q: How many tens are there in 100?

    A: There are 10 tens in 100, which is the result of dividing 100 by 10. This can be mathematically represented by the equation 100 / 10 = 10.
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  • What is 10 to the 8th power?

    Q: What is 10 to the 8th power?

    A: An exponent is how many times to use the number in a multiplication. Therefore, 10 to the 8th power is 100,000,000. It is solved by the equation 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10.
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