Question

How do you simplify $\dfrac{20{{b}^{10}}}{10{{b}^{20}}}$ ?

Answer 1

Hint: To solve these types of questions use the law of exponents to cancel and simplify any like terms from the denominator and numerator and then simply multiply all the values in the numerator and the denominator to get the final answer.

Complete step by step solution:
Given the expression:
$\dfrac{20{{b}^{10}}}{10{{b}^{20}}}$
Laws of exponents can prove to be very helpful while solving such questions.
If the bases are the same then, there are many operations that can be performed on their powers. Exponents are also referred to as powers or indices.
We can say that exponent represents how many times to multiply a given number to reach a specific value.
To simplify the given expression, we will use the laws of exponents that states that $\dfrac{{{a}^{m}}}{{{a}^{n}}}={{a}^{m-n}}$ and${{a}^{m}}{{a}^{n}}={{a}^{m+n}}$.
Simplifying and re-writing the above given expression by using the above mentioned law of exponents, we get,
$\Rightarrow \dfrac{20{{b}^{10}}}{10{{b}^{20}}}=\dfrac{20{{b}^{10-20}}}{10}$
Simplifying the above expression by adding the powers of the variable,
$\Rightarrow \dfrac{20{{b}^{10}}}{10{{b}^{20}}}=\dfrac{20{{b}^{-10}}}{10}$
Again, use the law of exponents ${{a}^{-m}}=\dfrac{1}{{{a}^{m}}}$ to further simplify the above expression,
$\Rightarrow \dfrac{20{{b}^{-10}}}{10}=\dfrac{20}{10{{b}^{10}}}$

Now, in the above expression, $20\;$ gets cancelled by $10\;$ since it is a multiple of $10\;$ . Therefore, on further simplifying and solving, we get,
$\Rightarrow \dfrac{20}{10{{b}^{10}}}=\dfrac{2}{{{b}^{10}}}$
Hence, on simplifying the expression given in the question which is $\dfrac{20{{b}^{10}}}{10{{b}^{20}}}$ , we get the final answer as $\dfrac{2}{{{b}^{10}}}$.

Note: A fraction can be defined as a representation of a part of a whole. A general fraction includes a numerator and a denominator which is non-zero. The numerator and denominator are separated by a slash or a line. Apart from general or common fractions, there are many other types of fractions as well, which include compound fractions, complex fractions, and mixed fractions.