Question

What does it mean that a number to the \[5^{th}\] or \[6^{th}\] power mean?

Answer 1

Hint: Here the given question is solved by using the concept of exponents and powers. The given question is about finding the mean a number to the \[5^{th}\] or \[6^{th}\] power mean. To conclude the statement, we can learn the concept with example. Before explaining this, let us know about the concept of exponent.

Complete step by step answer:
The exponent is defined as the power of a certain number that shows how many times that the number is multiplied itself.
For example, \[{{3}^{5}}=3\times 3\times 3\times 3\times 3\], in this example, we multiplied 3 by itself 5 times.
Hence, 3 is called a base and the 5 is called the exponent, the value \[{{3}^{5}}\] is known as ‘Power’.
Let us solve the given question.
The given question is does it mean a number to the \[5^{th}\] or \[6^{th}\] power mean.
The answer to the given problem is it means that the number is multiplied by itself that many times.
We know that the exponents represented as ‘A number n multiplied by itself x times.
We can also write above statement as a mathematical expression,
\[{{n}^{x}}=n\times n\times n\times n\times n................\left( x\_times \right)\]
Translating above explanation into an example,
\[\begin{align}
  & {{5}^{1}}=5 \\
 & {{5}^{2}}=5\times 5 \\
 & {{5}^{3}}=5\times 5\times 5 \\
 & {{5}^{4}}=5\times 5\times 5\times 5 \\
\end{align}\]
For any fractions/decimal’s exponents and zero, there will be a special case.
The number to a fraction is the ‘$k^{th}$ root of a number raised to $i^{th}$ power.
\[{{n}^{\dfrac{i}{k}}}=\sqrt[k]{{{n}^{i}}}\]
An exponent to zero is always equal to 1.
\[\begin{align}
  & {{1}^{0}}=1 \\
 & {{2}^{0}}=1 \\
 & ..... \\
 & {{n}^{0}}=1 \\
\end{align}\]
Hence, we can conclude that it means that the number is multiplied by itself that many times.

Note: Don’t be confused between the exponents and powers. Students should know how to apply the powers to the given individual terms. By following the basic rules of powers and exponents, we can easily solve the question in this topic.