Answer
398.7k+ views
Hint:The Question says about the Quotient rule of exponents which states that if we divide two exponents with the same base , we just then keep the base and subtract the powers . According to the question base will become our base and the exponent will be 8 and we have to write in the way as the quotient rule says but in 4 different ways by using only positive non zero exponents.
Complete step by step answer:
We will first set the base as 5 and exponent as 8 which must come by applying a quotient exponential rule.First we will find the four combinations of numbers such that the difference of both the exponents can be calculated as 8.By applying Quotient exponential rule – Here $x$ and $y$ are the exponents and their difference must be 8 while applying Quotient exponential rule .
$ \dfrac{{{5^x}}}{{{5^y}}}$
$\Rightarrow x - y = 8$
Now let us make the 4 pairs of combination such that it gives 8 when the powers with same base are subtracted like the following in different ways –
The numbers 9 and 1 make the difference of the number 8 as we wanted.
The numbers 10 and 2 make the difference of the number 8 as we wanted.
The numbers 15 and 7 make the difference of the number 8 as we wanted.
The numbers 1000 and 992 make the difference of the number 8 as we wanted .
We can write these as =>
$\dfrac{{{5^9}}}{{{5^1}}} \\
\Rightarrow\dfrac{{{5^{10}}}}{{{5^2}}} \\
\Rightarrow\dfrac{{{5^{15}}}}{{{5^7}}} \\
\therefore\dfrac{{{5^{1000}}}}{{{5^{992}}}}$
Note: Avoid negative exponents for easier calculations.If there is more than one term in brackets , with an power outside the brackets then the power is distributed to every term in the brackets.The variable in the denominator , numerator and exponent cannot be equal to 0.Through quotient rule we can simplify an algebraic expression with expressions.
Complete step by step answer:
We will first set the base as 5 and exponent as 8 which must come by applying a quotient exponential rule.First we will find the four combinations of numbers such that the difference of both the exponents can be calculated as 8.By applying Quotient exponential rule – Here $x$ and $y$ are the exponents and their difference must be 8 while applying Quotient exponential rule .
$ \dfrac{{{5^x}}}{{{5^y}}}$
$\Rightarrow x - y = 8$
Now let us make the 4 pairs of combination such that it gives 8 when the powers with same base are subtracted like the following in different ways –
The numbers 9 and 1 make the difference of the number 8 as we wanted.
The numbers 10 and 2 make the difference of the number 8 as we wanted.
The numbers 15 and 7 make the difference of the number 8 as we wanted.
The numbers 1000 and 992 make the difference of the number 8 as we wanted .
We can write these as =>
$\dfrac{{{5^9}}}{{{5^1}}} \\
\Rightarrow\dfrac{{{5^{10}}}}{{{5^2}}} \\
\Rightarrow\dfrac{{{5^{15}}}}{{{5^7}}} \\
\therefore\dfrac{{{5^{1000}}}}{{{5^{992}}}}$
Note: Avoid negative exponents for easier calculations.If there is more than one term in brackets , with an power outside the brackets then the power is distributed to every term in the brackets.The variable in the denominator , numerator and exponent cannot be equal to 0.Through quotient rule we can simplify an algebraic expression with expressions.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)