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Power Calculator
Reviewed by
BS Román Ramos
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Table of Contents
How to Use the Exponent Calculator
To use this online tool, you simply need to specify the base of the power and its exponent, whether it's a positive integer, a fractional one, or even a negative one.
Once you have entered all the requested fields, click on “Calculate”, and the calculator will return the result of the exponentiation within seconds.
What are Powers and What are They Used For
Powers are simply repeated multiplications and are formed by two elements: the exponent (n) and the base (a). The latter is the number that we will raise to the former.
$$a^n$$
When dealing with integers for simplicity, imagine that you have to multiply a number by itself several times, for example, multiplying the number 3, 4 times, it would be too laborious to write the operation like this:
$$3 \times 3 \times 3 \times 3$$
To speed up this mathematical process, you could use the power, which is nothing but a reformulation of the previous operation, redone in a simpler, faster, and more convenient way:
$$3 \times 3 \times 3 \times 3 = 3^4$$
If you want to express 33 verbally, the most appropriate way is to say “three raised to three” or “three raised to the third power” or the most used “three cubed”. If it were raised to 2, you should say “three squared”.
In summary: when we operate with integers, we know the power of a number as the multiplication of this number n times. Such operation is indicated with an, where a is the base and b is the exponent.
How to Calculate Simple Powers
When you have to deal with an operation involving powers, for example: 53, the first thing you should do is identify the two parts that make it up.
The “bottom” number, in our example 5, is the base, while the “top” number is the exponent.
Exponent = 0
If the exponent is 0 and the base is an integer, the result will always be 1. For example:
$$5^0 = 1, \quad 18522^0 = 1$$
Exponent = 1
Powers whose exponent is 1, will remain exactly as the base.
Other Exponents
To execute the calculation of a power, simply multiply the base by itself the number of times the exponent indicates, continuing with our example 53:
$$5 \times 5 \times 5 = 125$$
If you want to perform the operation by hand, or even in your head, our recommendation is to do it by multiplying the numbers two by two, that is:
$$5 \times 5 = 25; \quad 25 \times 5 = 125$$
How to Perform Operations with Powers
If you want to add or subtract powers, you will need as a fundamental requirement that both have the same base. This operation is a simplification.
Adding
We could affirm that:
$$6^3 + 6^3$$
Is equal to:
$$ (1)(6^3) + (1)(6^3)$$
Therefore, the result of the sum of these two powers would be equal to:
$$2(6^3)$$
If we add the results of the powers individually, it would be the same but twice, therefore, by multiplying it by two we would be simplifying the process.
It may seem a bit cumbersome and hard to digest, but with an example, it will surely become much clearer:
$$6^3 + 6^3 = (6)(6)(6) + (6)(6)(6) = 2 (6)(6)(6) = 2 6^3$$
Subtracting
For subtractions, the procedure would be practically the same as in addition, only that the numbers preceding the powers would be subtracted instead of added.
Multiplying
To multiply powers, it is essential that all of them have, at least, the base in common, then you simply add the exponents of all of them.
It is actually another simplification, let's go with an example:
$$(5^2)(5^4)(5^3)$$
Which is the same as:
$$[5\times5] [5\times5\times5\times5][5\times5\times5] = 5^9$$
If you need to multiply different exponents within parentheses, as it could be
$$ (4^2)^3$$
simply multiply both exponents among them, and you will obtain the definitive exponent, for example:
$$(4^2)^3 = (4^2)(4^2)(4^2) = 4^6 $$
As the base is always the same, you can add the different exponents to calculate the result.
When dealing with a power whose exponent is negative, you must convert the exponent into a positive number, and for that, you will need to reformulate it in the form of a fraction.
Guide yourself through the following examples:
$$4^{(-2)} = \frac{1}{4^2}$$
$$3(4^{(-2)}) =\frac{3}{4^2}$$
Dividing
To divide two powers with the same base subtract the exponents from each other. As division is the operation just opposite to multiplication, it is solved by doing just the opposite procedure.
What to Do with an Exponent That Contains Fractions
If we encounter a power whose exponent is written fractionally, as, for example, 41/2 we just need to know that it is as if it were the square root of that number, as long as it is raised to 1, that is:
$$4^{\frac{1}{2}}=\sqrt{4}=2$$
This premise can be extrapolated to all the fractional exponents you encounter.
If for example you find the number 8 raised to 1/3, it means that to solve it you will need to calculate the cube root of 8, in this case, the result would be 2.
This is fundamentally because raising to the power is the opposite procedure to the root.
A Final Reminder
When you are working with powers, one of the things you should keep in mind is that increasing the exponent of any of them will greatly increase the final result of the operation.
Therefore, even if the final result seems to be a disproportionate figure, do not reject it for that reason, as it could be correct.
On the other hand, do not forget that a power raised to 1 means that the whole number remains as it is, and if, on the other hand, it is raised to 0 it will always be 1.
How to Raise Powers on the Calculator
To conclude, you should remember that most calculators have at least one key to solve powers.
This function can be found in two ways, either with the command exp or using the key xn.
If your physical calculator is very old and does not have this function, you can always use one of ours which are also free.
And that's all you need to know to perform operations with powers, we have made the explanation in the simplest way, always step by step and guided with examples so that no one gets lost along the way.
If you liked the article, do not forget to share it on your social networks, so as to make all your contacts aware of the existence of this online calculator community.
