Answer
Verified
391.5k+ views
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 $6.6.6.6$
\[\Rightarrow \dfrac{1}{6.6.6.6} \]
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.
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 $6.6.6.6$
\[\Rightarrow \dfrac{1}{6.6.6.6} \]
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.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Change the following sentences into negative and interrogative class 10 english CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
Application to your principal for the character ce class 8 english CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE