Content

• Tips
• Warnings

Exponents are used when a number is multiplied by itself. Instead of ${ displaystyle 4 * 4 * 4 * 4 * 4}$Learn the correct terms and vocabulary for problems with exponents. Do you have an exponent, such as ${ displaystyle 2 ^ {3}}$Multiply the base the number of times by itself as indicated by the exponent. If you have to solve a power by hand, you start by rewriting it as a multiplication. You multiply the base by itself the number of times, as indicated by the exponent. So, you have ${ displaystyle 3 ^ {4}}$Solve an expression: Multiply the first two numbers for the product. For example, with ${ displaystyle 4 ^ {5}}$Multiply the answer from the first pair (16) by the next number. Keep multiplying the numbers to "grow" your exponent. Continuing with our example, we multiply 16 by the following 4 so that:

• ${ displaystyle 4 ^ {5} = 16 * 4 * 4 * 4}$Also try the following examples and check your answers with a calculator.
  • ${ displaystyle 8 ^ {2}}$Use the "exp,"Xn{ displaystyle x ^ {n}}You can only add or subtract power numbers if they have the same base and the same exponent. If you are dealing with identical bases and exponents, such as ${ displaystyle 4 ^ {5} + 4 ^ {5}}$Multiply numbers with the same base by adding the exponents. If you have two exponents with the same base, such as ${ displaystyle x ^ {2} * x ^ {5}}$Multiply an exponential number raised to another power, such as (X2)5{ displaystyle (x ^ {2}) ^ {5}}Think of negative exponents as fractions, or the reciprocal of the number. If you don't know what a reciprocal is, no problem. If you are dealing with a negative exponent, such as ${ displaystyle 3 ^ {2}$Divide two numbers with the same base by subtracting the exponents. Dividing is the opposite of multiplication, and while they are not solved exactly as the opposite, they are here. If you are dealing with the equation ${ displaystyle { frac {4 ^ {4}} {4 ^ {2}}}}$Try some practice problems to get used to working with power numbers. The following exercises practice everything that has been covered so far. For the answer, simply select the line containing the exercise.
    • ${ displaystyle 5 ^ {3}}$Treat power number fractions, such as X12{ displaystyle x ^ { frac {1} {2}}}Make the numerator a normal exponent for a mixed fraction.${ displaystyle x ^ { frac {5} {3}}}$You can add, subtract, and multiply fractions in the form of power numbers - just as you normally would. It is much easier to add or subtract the exponents before solving or converting them to square root numbers. If the base is the same and the exponent is the same, then you can just add and subtract them. If only the base is the same, you can multiply and divide the exponents as usual, as long as you take into account how you add and subtract fractions. For instance:
      • ${ displaystyle x ^ { frac {5} {3}} + x ^ { frac {5} {3}} = 2 (x ^ { frac {5} {3}})}$
      • ${ displaystyle x ^ { frac {5} {3}} * x ^ { frac {2} {3}} = x ^ { frac {7} {3}}}$

    Tips

    • Most calculators have an exponent button - pressed after entering the base - for solving power number problems. Usually this looks like a ^ or x ^ y.
    • "Simplify" in mathematics means do the operations necessary to get the simplest form of the expressions in question.
    • 1 is the identity element of exponents. That means that any real number raised to the power of 1 (to the first power) is the number itself, for example: ${ displaystyle 4 ^ {1} = 4.}$ It also holds that 1 is the identity element of multiplication (1 as a multiplier, such as ${ displaystyle 5 * 1 = 5}$), and of division (1 as dividend, like ${ displaystyle 5/1 = 5}$.
    • The base zero to zero (0) is not defined (English: dne, does not exist). Computers or calculators then give an "error" as a result. Remember that any number that is not zero, up to the power of 0, is always equal to 1, ${ displaystyle 4 ^ {0} = 1.}$
    • For example, higher math for imaginary numbers is, ${ displaystyle e ^ {a} ix = cosax + isinax}$, at which ${ displaystyle i = { sqrt {(}} - 1)}$; e is an irrational, continuous constant equal to 2.71828 ..., and a is an arbitrary constant. The proof can be found in most books on higher mathematics.

    Warnings

    • An exponential increase causes the product to rise faster and faster, so that the answer may seem wrong, when it is correct. (Check this by graphing an exponential function, for example: 2, if x has a series of different values).