# Exponents

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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• #### 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: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: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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• #### 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: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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• #### 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 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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• #### 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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• #### 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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• #### Q:What is 10 to the 100th power?

A: Ten to the 100th power is the number 1 followed by 100 zeros, also called a "googol." A googol exceeds the total number of atoms in the observable universe.
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• #### Q:What is the square root of 175?

A: The square root of 175 is approximately 13.23. A square root is a number that, when multiplied by itself, is equal to the number of which it is a root. When 13.23 is multiplied by 13.23, which is the same as 13.23 to the second power or 13.232, it is approximately equal to 175.
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• #### Q:How do you set up a mobile hotspot with your AT&T phone?

A: Any 4G or hotspot enabled AT&T phone can launch a mobile hotspot by following the instructions for the device being used on the AT&T website. The method of setting up the hotspot is different for each device, but each result in available Wi-Fi.
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• #### 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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• #### Q:What is the square root of 18 in simplified radical form?

A: The simplified radical form of the square root of 18 is written as 3 times the square root of 2. The simplified radical form of a square root can be found by factoring out the squares of whole numbers.
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• #### Q:What is a multiplier in math?

A: In mathematics, the term "multiplier" pertains to any number by which another number, known as the "multiplicand," is multiplied. The result of a multiplication operation is referred to as the "product."
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• #### 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 a ray in math?

A: In math, a ray is part of a line that has an endpoint at its starting point and extends in a certain direction into infinity. Drawing a ray involves placing a line with one endpoint and an arrow point on the other end. To name a ray, the convention is to use the letter at the starting point followed by a letter near the arrow point.
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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 simplify multiplying square roots with variables?

A: In order to simplify square roots with variables that are to be multiplied, treat the variables as factors. Once the radicands are factored completely, cancel any like terms and multiply the simplified square roots.
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• #### Q:What is 20 squared?

A: The number 20 squared is 20 times 20, or 400. To square a number means to multiply that number by itself. It is notated by writing the base number, which in this case is 20, with the number 2 in superscript after it.
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• #### 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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