Definitions for to the power of
to the pow·er of

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1. to the power ofpreposition

   Indicating an exponent.

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1. to the power of

   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". When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, bn is the product of multiplying n bases: The exponent is usually shown as a superscript to the right of the base. In that case, bn is called "b raised to the nth power", "b (raised) to the power of n", "the nth power of b", "b to the nth power", or most briefly as "b to the nth". Starting from the basic fact stated above that, for any positive integer n {\displaystyle n} , b n {\displaystyle b^{n}} is n {\displaystyle n} occurrences of b {\displaystyle b} all multiplied by each other, several other properties of exponentiation directly follow. In particular: In other words, when multiplying a base raised to one exponent by the same base raised to another exponent, the exponents add. From this basic rule that exponents add, we can derive that b 0 {\displaystyle b^{0}} must be equal to 1, as follows. For any n {\displaystyle n} , b 0 ⋅ b n = b 0 + n = b n {\displaystyle b^{0}\cdot b^{n}=b^{0+n}=b^{n}} . Dividing both sides by b n {\displaystyle b^{n}} gives b 0 = b n / b n = 1 {\displaystyle b^{0}=b^{n}/b^{n}=1} . The fact that b 1 = b {\displaystyle b^{1}=b} can similarly be derived from the same rule. For example, ( b 1 ) 3 = b 1 ⋅ b 1 ⋅ b 1 = b 1 + 1 + 1 = b 3 {\displaystyle (b^{1})^{3}=b^{1}\cdot b^{1}\cdot b^{1}=b^{1+1+1}=b^{3}} . Taking the cube root of both sides gives b 1 = b {\displaystyle b^{1}=b} . The rule that multiplying makes exponents add can also be used to derive the properties of negative integer exponents. Consider the question of what b − 1 {\displaystyle b^{-1}} should mean. In order to respect the "exponents add" rule, it must be the case that b − 1 ⋅ b 1 = b − 1 + 1 = b 0 = 1 {\displaystyle b^{-1}\cdot b^{1}=b^{-1+1}=b^{0}=1} . Dividing both sides by b 1 {\displaystyle b^{1}} gives b − 1 = 1 / b 1 {\displaystyle b^{-1}=1/b^{1}} , which can be more simply written as b − 1 = 1 / b {\displaystyle b^{-1}=1/b} , using the result from above that b 1 = b {\displaystyle b^{1}=b} . By a similar argument, b − n = 1 / b n {\displaystyle b^{-n}=1/b^{n}} . The properties of fractional exponents also follow from the same rule. For example, suppose we consider b {\displaystyle {\sqrt {b}}} and ask if there is some suitable exponent, which we may call r {\displaystyle r} , such that b r = b {\displaystyle b^{r}={\sqrt {b}}} . From the definition of the square root, we have that b ⋅ b = b {\displaystyle {\sqrt {b}}\cdot {\sqrt {b}}=b} . Therefore, the exponent r {\displaystyle r} must be such that b r ⋅ b r = b {\displaystyle b^{r}\cdot b^{r}=b} . Using the fact that multiplying makes exponents add gives b r + r = b {\displaystyle b^{r+r}=b} . The b {\displaystyle b} on the right-hand side can also be written as b 1 {\displaystyle b^{1}} , giving b r + r = b 1 {\displaystyle b^{r+r}=b^{1}} . Equating the exponents on both sides, we have r + r = 1 {\displaystyle r+r=1} . Therefore, r = 1 2 {\displaystyle r={\frac {1}{2}}} , so b = b 1 / 2 {\displaystyle {\sqrt {b}}=b^{1/2}} . The definition of exponentiation can be extended to allow any real or complex exponent. Exponentiation by integer exponents can also be defined for a wide variety of algebraic structures, including matrices. Exponentiation is used extensively in many fields, including economics, biology, chemistry, physics, and computer science, with applications such as compound interest, population growth, chemical reaction kinetics, wave behavior, and public-key cryptography.

How to pronounce to the power of?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say to the power of in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of to the power of in Chaldean Numerology is: 5

2. Pythagorean Numerology

   The numerical value of to the power of in Pythagorean Numerology is: 4

Examples of to the power of in a Sentence

1. Chris Norman:

   I'm not an expert in the area but I do think we need to figure out how to harness the power of the citizens.

2. Lisa Grennan:

   A dog the size of the Hulk could kill someone if it was in the wrong situation at the wrong time, the power of this dog is unrivalled. If he bit down on someone's arm with full power it would snap like a toothpick.

3. Ronnie Shakes:

   I was going to buy a copy of "The Power of Positive Thinking", and then I thought: What the hell good would that do?

4. Helen Keller:

   Tyranny cannot defeat the power of ideas.

5. Marcel Aubut:

   It is time to make it crystal clear. I am officially declaring that I will use the full power of my office to lead and advocate for Toronto's candidacy to hold the 2024 Olympic Games, this is it.

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/To_the_Power_of
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/To_the_Power_of