
What is the value of ${{a}^{-5}}\times {{a}^{0}}\times {{a}^{5}}$?
Answer
549k+ views
Hint: Any number $x$ if raised to the power of a number $-y$, then this is equal to the reciprocal of $x$ raised to the power of $y$: i.e. ${{x}^{-y}}=\dfrac{1}{{{x}^{y}}}$ .
Complete step by step solution:
In this question, we need to find the value of ${{a}^{-5}}\times {{a}^{0}}\times {{a}^{5}}$
We already know the property that any number $x$ if raised to the power of a number $-y$,
then this is equal to the reciprocal of $x$ raised to the power of $y$:
i.e. ${{x}^{-y}}=\dfrac{1}{{{x}^{y}}}$
Using this property, we will rewrite the given expression.
After rewriting, we will get the following:
$\dfrac{1}{{{a}^{5}}}\times {{a}^{0}}\times {{a}^{5}}$
We will now rearrange the above expression as:
$\left( \dfrac{1}{{{a}^{5}}}\times {{a}^{5}} \right)\times {{a}^{0}}$
Now, we also know the property that any number x when multiplied by its reciprocal will
give the product as 1.
i.e. $x\times \dfrac{1}{x}=1$
We will use this property on the above expression to get the following:
$\left( \dfrac{1}{{{a}^{5}}}\times {{a}^{5}} \right)\times {{a}^{0}}=1\times {{a}^{0}}={{a}^{0}}$
So, we get the following expression:
${{a}^{-5}}\times {{a}^{0}}\times {{a}^{5}}={{a}^{0}}$
Now, we need to find the value of ${{a}^{0}}$
We know that any number x raised to the power of zero is equal to 1.
i.e. ${{x}^{0}}=1$ , where $x$ is any number.
Using this property, we will get the following:
${{a}^{0}}=1$
Hence, we arrive at the following final expression:
${{a}^{-5}}\times {{a}^{0}}\times {{a}^{5}}=1$
So, our final answer is ${{a}^{-5}}\times {{a}^{0}}\times {{a}^{5}}=1$.
Note: In this question, it is very important to identify which property to use and how to use
it. You need to rearrange the terms properly in order to see and understand the problem
clearly.
Complete step by step solution:
In this question, we need to find the value of ${{a}^{-5}}\times {{a}^{0}}\times {{a}^{5}}$
We already know the property that any number $x$ if raised to the power of a number $-y$,
then this is equal to the reciprocal of $x$ raised to the power of $y$:
i.e. ${{x}^{-y}}=\dfrac{1}{{{x}^{y}}}$
Using this property, we will rewrite the given expression.
After rewriting, we will get the following:
$\dfrac{1}{{{a}^{5}}}\times {{a}^{0}}\times {{a}^{5}}$
We will now rearrange the above expression as:
$\left( \dfrac{1}{{{a}^{5}}}\times {{a}^{5}} \right)\times {{a}^{0}}$
Now, we also know the property that any number x when multiplied by its reciprocal will
give the product as 1.
i.e. $x\times \dfrac{1}{x}=1$
We will use this property on the above expression to get the following:
$\left( \dfrac{1}{{{a}^{5}}}\times {{a}^{5}} \right)\times {{a}^{0}}=1\times {{a}^{0}}={{a}^{0}}$
So, we get the following expression:
${{a}^{-5}}\times {{a}^{0}}\times {{a}^{5}}={{a}^{0}}$
Now, we need to find the value of ${{a}^{0}}$
We know that any number x raised to the power of zero is equal to 1.
i.e. ${{x}^{0}}=1$ , where $x$ is any number.
Using this property, we will get the following:
${{a}^{0}}=1$
Hence, we arrive at the following final expression:
${{a}^{-5}}\times {{a}^{0}}\times {{a}^{5}}=1$
So, our final answer is ${{a}^{-5}}\times {{a}^{0}}\times {{a}^{5}}=1$.
Note: In this question, it is very important to identify which property to use and how to use
it. You need to rearrange the terms properly in order to see and understand the problem
clearly.
Recently Updated Pages
Master Class 9 General Knowledge: Engaging Questions & Answers for Success

Master Class 9 English: Engaging Questions & Answers for Success

Master Class 9 Maths: Engaging Questions & Answers for Success

Master Class 9 Social Science: Engaging Questions & Answers for Success

List of National & International Important Days

Master Class 10 Computer Science: Engaging Questions & Answers for Success

Trending doubts
Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Name 10 Living and Non living things class 9 biology CBSE

The highest mountain peak in India is A Kanchenjunga class 9 social science CBSE

On an outline map of India show its neighbouring c class 9 social science CBSE

Write the 6 fundamental rights of India and explain in detail
