# What is the value of ${{a}^{-5}}\times {{a}^{0}}\times {{a}^{5}}$?

Last updated date: 21st Mar 2023

•

Total views: 305.4k

•

Views today: 7.84k

Answer

Verified

305.4k+ 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

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

A Short Paragraph on our Country India