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Exponentiation

Tool to compute power of a number. Exponentiation (or power) of a number 'a^b' is the result of the 'b'-times repeated multiplication of the number 'a' by itself.

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Exponentiation -

Tag(s) : Arithmetics

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Exponentiation

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Tool to compute power of a number. Exponentiation (or power) of a number 'a^b' is the result of the 'b'-times repeated multiplication of the number 'a' by itself.

Answers to Questions

How to calculate a raised to power b?

Calculating \( a \) power \( b \) (also called \( a \) exponent \( b \)) corresponds to multiply \( a \) by itself \( b \) times.

$$ a^n = \underbrace{a \times \cdots \times a}_{b\ times} $$

Example: $$ 2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32 $$

What are the base and the exponent in an exponentiation? (Definition)

In a power calculation \( a^b = c \), the part \( a \) is called the base and the part \( b \) is called the exponent, \( c \) is normally called power but in everyday language power and exponentiation are often exchanged.

What are power tables?

Like the multiplication tables, there is a, exponentiation table, or table of powers but this one is not symmetrical (a^b is not always equal to b^a). Here is the table reading row^column:

\012345678910
010000000000
111111111111
212481632641282565121024
31392781243729218765611968359049
41416642561024409616384655362621441048576
515251256253125156257812539062519531259765625
61636216129677764665627993616796161007769660466176
71749343240116807117649823543576480140353607282475249
818645124096327682621442097152167772161342177281073741824
919817296561590495314414782969430467213874204893486784401
10110100100010000100000100000010000000100000000100000000010000000000

How to write a raised to power b?

In mathematics, a power is written \( a \) exponent \( b \) as \( a^b \).

In computing, the exponentiation calculation is often indicated by a circumflex ^ : a^b for a power b. In some programming languages, the notation a**b (the multiplication sign twice) is used.

What is a negative power?

A negative power is the inverse of a positive power.

Example: \( a^{-2} = \frac{1}{a^2} \)

What is the minus one -1 power?

The power -1 in maths is equivalent to a mathematical inverse.

Example: \( n^{-1} = \frac{1}{n^1} = \frac{1}{n} \)

Why exponent has to be an integer and not rational?

Exponent corresponds to the number of times the multiplication has to be done. If the exponent is not an integer, it becomes a root calculus and is not managed by this function. Use the formal calculator on dCode.

What are exponentiation operation properties?

The exponentiation operator has 3 main mathematical identities:

$$ a^{b + c} = a^b \cdot a^c \\ (a^b)^n = a^{b \cdot n} \\ (a \cdot b)^n = a^n \cdot b^n $$

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