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The Exponentiation Calculator will calculate:

- The power of a number
- The power of a number by rounding the result to the correct number of significant figures
- The power of a number by rounding the result to the correct number of decimal places

**Exponentiation Calculator Parameters:**

Result of exponentiation |

Result of exponentiation to significant figures |

Result of exponentiation rounded to decimal places |

Exponentiation Calculator Input Values |
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Base of exponentiation (b) = |

Exponent (n) = |

Please note that the formula for each calculation along with detailed calculations is shown further below this page. As you enter the specific factors of each exponentiation calculation, the Exponentiation Calculator will automatically calculate the results and update the formula elements with each element of the exponentiation calculation. You can then email or print this exponentiation calculation as required for later use.

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Exponentiation is a mathematical operation, written as bn, involving two numbers, the base b and the exponent or power n, and pronounced as "b raised to the power of n". It represents a repeated multiplication of b × b × b × by n times. For example, 3^{4} = 81 because 3 × 3 × 3 × 3 = 81.

When the exponent n is negative, the result of exponentiation is usually small as the following property of exponentiation is applied:

b^{-n} = *1**/**b*^{n}

5^{-3} = *1**/**5*^{3} = *1**/**125* = 0.008

In exponentiation, the base is considered as known and accurately measured. In the case when base is an irrational number such as any irrational square root (√2, √3, √5 etc.), we can apply the following property of exponentiation

b^{a∙x} = (b^{a})^{n}

to remove the square root from the expression, in order to obtain a finite and exact base. Thus, we obtain

b^{n} = (b^{2} )^{n/2}

(√**2**)^{13}

we can write this exponentiation as

[(√**2**)^{2} ]^{13/2} = 2^{6.5} = 90.50966799

Obviously, this result must be rounded in some way. In chemistry, exponentiation (bn) only rounds by the significant figures in the base. Thus, the above result is written in 1 s.f. by rounding it as 90. This is because despite the number being closer to 91, we round it to 90 to express the result to 1 s.f. as the base (2) has only 1 s.f.

(√**278**)^{2.3} = [(√**278**)^{2} ]^{2.3/2} = 278^{1.15} = 646.62354666057

In this case, we have to write the result in 3 s.f. because the base contain 3 s.f: 2, 7 and 8. Therefore, the result of operation (based on the rounding rules) is 647.

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