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 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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  • 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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  • 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 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 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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  • 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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  • Q: What is a list of perfect square roots?

    A: A perfect square-root chart lists the integer roots of numbers that have no fractional component. Multiplying these square roots by themselves results in designated perfect squares. For example, the square root of nine is three. Nine is a perfect square and three is a perfect square root.
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  • Q: What is the square root of 121?

    A: The square root of 121 is 11 or negative 11. The factors of 121 are 11 x 11. Similarly, negative 11 x negative 11 is also 121. To obtain an exact square root, the number must be a perfect square.
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  • How do you simplify cube roots?

    Q: How do you simplify cube roots?

    A: Simplify a cube root expression by factoring out the cube of a whole number if one is present. Continue factoring until the expression no longer contains the cube of a whole number, and solve for any cube roots of whole numbers that are present.
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  • Q: What is the square root of 125?

    A: The square root of 125 is approximately 11.18. The decimals of the exact answer go on infinitely because the square root of 125 is an irrational number.
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  • Q: What is the square root of 28?

    A: The square root of 28 is 5.29, rounded to two decimal places, as 28 is not a perfect square. The square root of a perfect square is a whole number and not a decimal or fraction. The square root of 25 is 5, as 25 is a perfect square.
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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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  • What are distributing exponents?

    Q: What are distributing exponents?

    A: The distributive property of exponents is a mathematical rule that applies to an exponent that acts on a term that is within parentheses. It says that if there is a single term in the base, such as "3x," and it is raised to a certain power, like "(3x)^6," the exponent applies to all parts of the term, in this case to both the three and the "x."
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  • Q: What is the prime factorization of 49?

    A: The prime factorization of 49 is equal to 7*7. The prime factorization of a number is a way of representing a number as the result of two or more prime factors.
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  • Q: What is the square root of 109?

    A: The square root of 109 is 10.44. The square root is expressed through the formula x times x equals y, where x is the square root of y. Plugging the number 109 into the equation results in 10.44 times 10.44 equals 109.
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  • Q: What are perfect square trinomials?

    A: A perfect square trinomial is a polynomial with three terms that is expanded or FOILed form of a binomial squared. Taking the square root of a perfect square trinomial will result in a rational expression, unlike the roots of other trinomials.
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  • What is a method for multiplying fractions with exponents?

    Q: What is a method for multiplying fractions with exponents?

    A: A good method for multiplying fractions with exponents is to factor, cancel and simplify. This works whether the exponent is attached to a variable or a numeral.
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  • Q: What are some of the multiples of 32?

    A: The first 10 multiples of 32 are 32, 64, 96, 128, 160, 192, 224, 256, 288 and 320. A multiple is the original number multiplied by an integer, which is a number that is not a fraction.
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