Answer
414.6k+ views
Hint: To divide the exponents or the powers with the same base or the same term, simply subtract the powers. As, the division is just the opposite of the multiplication, so when you add the powers in the multiplication, just subtract the powers in case of the division with the same base. For example \[{{2}^{5}}\div {{2}^{2}}={{2}^{5-2}}={{2}^{3}}\]
Complete step-by-step answer:
Here, by using the property – in case of division of the powers with the same base, simply subtracting the powers
$\Rightarrow {{\left( \dfrac{-5}{6} \right)}^{\dfrac{3}{4}}}\div {{\left( \dfrac{-5}{6} \right)}^{\dfrac{7}{6}}}={{\left( \dfrac{-5}{6} \right)}^{\dfrac{3}{4}-\dfrac{7}{6}}}$
Take LCM of the powers on the right hand side of the equation
$\Rightarrow {{\left( \dfrac{-5}{6} \right)}^{\dfrac{3}{4}}}\div {{\left( \dfrac{-5}{6} \right)}^{\dfrac{7}{6}}}={{\left( \dfrac{-5}{6} \right)}^{\dfrac{18}{24}-\dfrac{28}{24}}}$
Now, simply the power on the right hand side of the equation. Using the identity of minus and plus, do minus and sign of greater value.
$\Rightarrow {{\left( \dfrac{-5}{6} \right)}^{\dfrac{3}{4}}}\div {{\left( \dfrac{-5}{6} \right)}^{\dfrac{7}{6}}}={{\left( \dfrac{-5}{6} \right)}^{\dfrac{-10}{24}}}$
Taking “two common” from the numerator and denominator of the power on RHS
$\Rightarrow {{\left( \dfrac{-5}{6} \right)}^{\dfrac{3}{4}}}\div {{\left( \dfrac{-5}{6} \right)}^{\dfrac{7}{6}}}={{\left( \dfrac{-5}{6} \right)}^{\dfrac{-5}{12}}}$
Therefore, the required solution is –
$\Rightarrow {{\left( \dfrac{-5}{6} \right)}^{\dfrac{3}{4}}}\div {{\left( \dfrac{-5}{6} \right)}^{\dfrac{7}{6}}}={{\left( \dfrac{-5}{6} \right)}^{\dfrac{-5}{12}}}$
Note: Always remember all the rules of multiplication and division of the fractions. Remember two basic rules - Multiply the given terms with the exponents using the general rule: ${{y}^{a}}\times {{y}^{b}}={{y}^{a+b}}$ and similarly the divide terms with the exponents using the rule: ${{y}^{a}}\div {{y}^{b}}={{y}^{a-b}}$. Do simplification carefully. Rest goes perfect in these types of questions.
Complete step-by-step answer:
Here, by using the property – in case of division of the powers with the same base, simply subtracting the powers
$\Rightarrow {{\left( \dfrac{-5}{6} \right)}^{\dfrac{3}{4}}}\div {{\left( \dfrac{-5}{6} \right)}^{\dfrac{7}{6}}}={{\left( \dfrac{-5}{6} \right)}^{\dfrac{3}{4}-\dfrac{7}{6}}}$
Take LCM of the powers on the right hand side of the equation
$\Rightarrow {{\left( \dfrac{-5}{6} \right)}^{\dfrac{3}{4}}}\div {{\left( \dfrac{-5}{6} \right)}^{\dfrac{7}{6}}}={{\left( \dfrac{-5}{6} \right)}^{\dfrac{18}{24}-\dfrac{28}{24}}}$
Now, simply the power on the right hand side of the equation. Using the identity of minus and plus, do minus and sign of greater value.
$\Rightarrow {{\left( \dfrac{-5}{6} \right)}^{\dfrac{3}{4}}}\div {{\left( \dfrac{-5}{6} \right)}^{\dfrac{7}{6}}}={{\left( \dfrac{-5}{6} \right)}^{\dfrac{-10}{24}}}$
Taking “two common” from the numerator and denominator of the power on RHS
$\Rightarrow {{\left( \dfrac{-5}{6} \right)}^{\dfrac{3}{4}}}\div {{\left( \dfrac{-5}{6} \right)}^{\dfrac{7}{6}}}={{\left( \dfrac{-5}{6} \right)}^{\dfrac{-5}{12}}}$
Therefore, the required solution is –
$\Rightarrow {{\left( \dfrac{-5}{6} \right)}^{\dfrac{3}{4}}}\div {{\left( \dfrac{-5}{6} \right)}^{\dfrac{7}{6}}}={{\left( \dfrac{-5}{6} \right)}^{\dfrac{-5}{12}}}$
Note: Always remember all the rules of multiplication and division of the fractions. Remember two basic rules - Multiply the given terms with the exponents using the general rule: ${{y}^{a}}\times {{y}^{b}}={{y}^{a+b}}$ and similarly the divide terms with the exponents using the rule: ${{y}^{a}}\div {{y}^{b}}={{y}^{a-b}}$. Do simplification carefully. Rest goes perfect in these types of questions.
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)