Answer
385.5k+ views
Hint: This problem can be solved using law of indices.
${{a}^{m}} \times {{a}^{n}}={{a}^{m+n}}$ This is first law of indices which states that when the two terms have the same base and the terms have to multiplied together then their indices are added.
${{\left( ab \right)}^{n}}={{a}^{n}}.{{b}^{n}}$ In this formula the powers of the terms are separated and given to each. These two formulas will help you in solving problems.
Complete step by step solution:
Here, we have to write $''4x$ (times) $4x$ (times) $4x''$ in exponential form.
That is we have to write $4x.4x.4x$ in exponential form.
Now, $4x$ can be written as also ${{\left( 4x \right)}^{2}}$
Therefore, $4x={{\left( 4x \right)}^{1}}$
So, we have.
$\Rightarrow \left( 4x.4x.4x \right)={{\left( 4x \right)}^{1}}{{\left( 4x \right)}^{1}}{{\left( 4x \right)}^{1}}$
We know that, when multiplying the exponents having the same base value, we have to simply add their power and take base value as common. That is we can write above equation as,
$\left( 4x.4x.4x \right)={{\left( 4x \right)}^{1}}{{\left( 4x \right)}^{1}}{{\left( 4x \right)}^{1}}$
Now,
Taking base as common and adding the power then equation will be,
$\left( 4x.4x.4x \right)={{\left( 4x \right)}^{\left( 1+1+1 \right)}}$
$\Rightarrow \left( 4x.4x.4x \right)={{\left( 4x \right)}^{3}}$
Now, separating the power of term ${{\left( 4x \right)}^{3}}$ then we have,
$\left( 4x.4x.4x \right)={{4}^{3}}{{x}^{3}}$
As we know that,
${{4}^{3}}=4\times 4\times 4=64$ and keeping ${{x}^{3}}$ as it is.
Therefore we have the equation as.
$\left( 4x.4x.4x \right)=64{{x}^{3}}$
Hence, $''4x$ $\times$ $4x$ $\times$ $4x''$ in exponential form can be written as $64{{x}^{3}}$
The term exponential means the number of times a number multiplied by itself. Here, we multiply the numbers and convert into the simplest and short form of exponential. Use laws of indices for solving problems.
Note: We have to take precaution when multiplying the exponents term with the same base value. We have not to multiply the power of bases. We have to take base value as common and perform addition of their powers only.
${{a}^{m}} \times {{a}^{n}}={{a}^{m+n}}$ This is first law of indices which states that when the two terms have the same base and the terms have to multiplied together then their indices are added.
${{\left( ab \right)}^{n}}={{a}^{n}}.{{b}^{n}}$ In this formula the powers of the terms are separated and given to each. These two formulas will help you in solving problems.
Complete step by step solution:
Here, we have to write $''4x$ (times) $4x$ (times) $4x''$ in exponential form.
That is we have to write $4x.4x.4x$ in exponential form.
Now, $4x$ can be written as also ${{\left( 4x \right)}^{2}}$
Therefore, $4x={{\left( 4x \right)}^{1}}$
So, we have.
$\Rightarrow \left( 4x.4x.4x \right)={{\left( 4x \right)}^{1}}{{\left( 4x \right)}^{1}}{{\left( 4x \right)}^{1}}$
We know that, when multiplying the exponents having the same base value, we have to simply add their power and take base value as common. That is we can write above equation as,
$\left( 4x.4x.4x \right)={{\left( 4x \right)}^{1}}{{\left( 4x \right)}^{1}}{{\left( 4x \right)}^{1}}$
Now,
Taking base as common and adding the power then equation will be,
$\left( 4x.4x.4x \right)={{\left( 4x \right)}^{\left( 1+1+1 \right)}}$
$\Rightarrow \left( 4x.4x.4x \right)={{\left( 4x \right)}^{3}}$
Now, separating the power of term ${{\left( 4x \right)}^{3}}$ then we have,
$\left( 4x.4x.4x \right)={{4}^{3}}{{x}^{3}}$
As we know that,
${{4}^{3}}=4\times 4\times 4=64$ and keeping ${{x}^{3}}$ as it is.
Therefore we have the equation as.
$\left( 4x.4x.4x \right)=64{{x}^{3}}$
Hence, $''4x$ $\times$ $4x$ $\times$ $4x''$ in exponential form can be written as $64{{x}^{3}}$
The term exponential means the number of times a number multiplied by itself. Here, we multiply the numbers and convert into the simplest and short form of exponential. Use laws of indices for solving problems.
Note: We have to take precaution when multiplying the exponents term with the same base value. We have not to multiply the power of bases. We have to take base value as common and perform addition of their powers only.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 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)
Give 10 examples for herbs , shrubs , climbers , creepers
![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)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english 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)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)