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what is the value of power $6^{-4} $?

Last updated date: 18th Jul 2024
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Hint: Well, the answer to this question is solved based on the concept of power. The given question is solved by taking the $6^{-4} $ into reciprocal form with the help of basic formula and expanding the form and calculating the desired result.

Complete step by step solution:
Concept of the power: The power is defined as the ‘a’ be any number and ‘n’ is natural number, then the formula is
\[a^{n} =aaa.........\]
Here a is called as ‘base’ and ‘n’ is known as index or exponent, and is called as exponential expression and it can be read as ‘a to the power of n’.
In the given problem, $6^{-4} $ is the negative exponent.
Negative exponent is defined as If the exponent is negative, it implies that the reciprocal of the positive exponent is negative. To put it another way, it means doing the inverse of multiplication, which is division.
The algebraic expression for Negative exponent is
\[x^{-n} =\dfrac{1}{x^{n} } \]
 which can be written as in the below form
$\Rightarrow $$x^{n} =xxxx......$ (n times)
Based on the formula, we are going to solve the given problem
$6^{-4} $ is going to write in reciprocal form
\[6^{-4} =\dfrac{1}{6^{4} } \]
Writing $6^{4} $into expanded form as $$
\[\Rightarrow \dfrac{1}{} \]
Which is equal to
\[\Rightarrow \dfrac{1}{1296} \]
\[\Rightarrow 0.000771...\]
The value of$ \textbf{ }6^{-4} $is $0.000771…$.

Note: The most common error made by students is incorrect multiplication. Multiplying two or more factors with the same base by adding (rather than multiplying) the exponents is also possible. Multiplying the exponents, at least for positive integer powers, is another mistake.