Courses
Courses for Kids
Free study material
Offline Centres
More

# How do you write 5 ( to the power of 8 ) as a quotient of 2 exponential terms with the same base in 4 different ways by using only positive non zero exponents ?

Last updated date: 26th Feb 2024
Total views: 340.2k
Views today: 7.40k
Verified
340.2k+ 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.

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 .
$\dfrac{{{5^x}}}{{{5^y}}}$
$\Rightarrow x - y = 8$
$\dfrac{{{5^9}}}{{{5^1}}} \\ \Rightarrow\dfrac{{{5^{10}}}}{{{5^2}}} \\ \Rightarrow\dfrac{{{5^{15}}}}{{{5^7}}} \\ \therefore\dfrac{{{5^{1000}}}}{{{5^{992}}}}$