Courses
Courses for Kids
Free study material
Offline Centres
More
Store

# Find:${{\left( \dfrac{-5}{6} \right)}^{\dfrac{3}{4}}}\div {{\left( \dfrac{-5}{6} \right)}^{\dfrac{7}{6}}}$

Last updated date: 16th Jun 2024
Total views: 402.6k
Views today: 5.02k
Verified
402.6k+ 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 ${{2}^{5}}\div {{2}^{2}}={{2}^{5-2}}={{2}^{3}}$

$\Rightarrow {{\left( \dfrac{-5}{6} \right)}^{\dfrac{3}{4}}}\div {{\left( \dfrac{-5}{6} \right)}^{\dfrac{7}{6}}}={{\left( \dfrac{-5}{6} \right)}^{\dfrac{3}{4}-\dfrac{7}{6}}}$
$\Rightarrow {{\left( \dfrac{-5}{6} \right)}^{\dfrac{3}{4}}}\div {{\left( \dfrac{-5}{6} \right)}^{\dfrac{7}{6}}}={{\left( \dfrac{-5}{6} \right)}^{\dfrac{18}{24}-\dfrac{28}{24}}}$
$\Rightarrow {{\left( \dfrac{-5}{6} \right)}^{\dfrac{3}{4}}}\div {{\left( \dfrac{-5}{6} \right)}^{\dfrac{7}{6}}}={{\left( \dfrac{-5}{6} \right)}^{\dfrac{-10}{24}}}$
$\Rightarrow {{\left( \dfrac{-5}{6} \right)}^{\dfrac{3}{4}}}\div {{\left( \dfrac{-5}{6} \right)}^{\dfrac{7}{6}}}={{\left( \dfrac{-5}{6} \right)}^{\dfrac{-5}{12}}}$
$\Rightarrow {{\left( \dfrac{-5}{6} \right)}^{\dfrac{3}{4}}}\div {{\left( \dfrac{-5}{6} \right)}^{\dfrac{7}{6}}}={{\left( \dfrac{-5}{6} \right)}^{\dfrac{-5}{12}}}$
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.