Free Study Material

NCERT Solutions

NCERT Books

Revision Notes

Practice Problems

This is one of our many quizzes on types of exponents. Click on this to access more such competitive quizzes on exponents.

Types of Exponents Quiz 2

mathematics

 Evaluate $\dfrac{{ - 15p{q^8}}}{{3{p^{ - 4}}{q^2}}} \times \dfrac{{8{p^{ - 3}}{q^5}}}{{{{\left( { - 2q} \right)}^3}}}$.

 Use the rules ${a^m} \times {a^n} = {a^{m + n}}$ and $\dfrac{{{a^m}}}{{{a^n}}} = {a^{m - n}}$.

$  {\text{ }}\dfrac{{ - 15p{q^8}}}{{3{p^{ - 4}}{q^2}}} \times \dfrac{{8{p^{ - 3}}{q^5}}}{{{{\left( { - 2q} \right)}^3}}} \\   \Rightarrow \dfrac{{ - 120{p^{ - 2 + 4}}{q^{13 - 5}}}}{{ - 6}} \\   \Rightarrow \left( {20 \times {p^2} \times {q^8}} \right) \\  $

 Solve the expression $\dfrac{{36 \times {p^{ - 2}}}}{{{{\left( {\sqrt 6 } \right)}^{ - 4}} \times {6^{ - 3}} \times {p^{ - 4}}}}$.

 Use the degree rules in multiply, ${a^m} \times {a^n} = {a^{m + n}}$ and $\dfrac{{{a^m}}}{n} = {a^{m - n}}$.

$  \dfrac{{36 \times {p^{ - 2}}}}{{{{\left( {\sqrt 6 } \right)}^{ - 4}} \times {6^{ - 3}} \times {p^{ - 4}}}} \Rightarrow \dfrac{{{{\left( 6 \right)}^2} \times {p^4}}}{{{{\left( 6 \right)}^{ - 2}} \times {6^{ - 3}} \times {p^2}}} \\   \Rightarrow {6^2} \times {6^2} \times {6^3} \times {p^{4 - 2}} \\   \Rightarrow {6^7} \times {p^2} \\  $

 Evaluate ${\left( {\dfrac{1}{2} + \dfrac{1}{3}} \right)^2} \times {\left( {\dfrac{1}{3} - \dfrac{1}{4}} \right)^2}$

 Use ${x^{ - m}} \times \dfrac{1}{{{x^m}}}$ and then simplify the given expression.

$  {\left( {\dfrac{{3 + 2}}{6}} \right)^2} \times {\left( {\dfrac{{4 - 3}}{{12}}} \right)^2} \\   \Rightarrow \dfrac{{5 \times 5}}{{6 \times 6}} \times \dfrac{{12 \times 12}}{1} = 100 \\  $

 If $u = \dfrac{{ - 1331}}{{729}},\,\,v = \dfrac{{343}}{{125}}$ and $w = \dfrac{{16}}{{81}}$, then evaluate ${u^{\frac{1}{3}}} + {v^{\frac{2}{3}}} + {w^{\frac{1}{4}}}$.

 Convert the given numbers into the highest exponential form.

${u^{\frac{1}{3}}} + {v^{\frac{2}{3}}} + {w^{\frac{1}{4}}}$ Putting the values and taking their roots we get $ \\ \Rightarrow  - \left( {\dfrac{{11}}{9}} \right) + \left( {\dfrac{7}{5}} \right) + \left( {\dfrac{2}{3}} \right) \\   \Rightarrow \dfrac{{ - 11}}{9} + \dfrac{{49}}{{25}} + \dfrac{2}{3} \\   \Rightarrow \dfrac{{316}}{{225}} \\  $

 Evaluate ${\left( {\sqrt p } \right)^{\frac{{ - 2}}{7}}}\left( {\sqrt {{q^8}} } \right) \div \sqrt {{{\left( {pq} \right)}^{\frac{{ - 1}}{3}}}} $

 Convert to simplify form and use the quotient rules: ${a^m} \div {a^n} = {a^{m - n}}$.

$  {\left( {{{\left( p \right)}^{\frac{1}{2}}}} \right)^{\frac{{ - 2}}{7}}}{\left( {{q^8}} \right)^{\frac{1}{2}}} \div {\left( {{{\left( {pq} \right)}^{\frac{{ - 1}}{3}}}} \right)^{\frac{1}{2}}} \\   \Rightarrow {\left( p \right)^{\frac{1}{2} \times \frac{{ - 2}}{7}}}{\left( q \right)^{8 \times \frac{1}{2}}} \div {\left( {pq} \right)^{\frac{{ - 1}}{3} \times \frac{1}{2}}} \\   \Rightarrow {\left( p \right)^{\frac{{ - 1}}{7}}}{\left( q \right)^4} \div {\left( p \right)^{\frac{{ - 1}}{6}}}{\left( q \right)^{\frac{{ - 1}}{6}}} \\   \Rightarrow {\left( p \right)^{\frac{{ - 1}}{7} + \frac{1}{6}}}{\left( q \right)^{4 + \frac{1}{6}}} \\   \Rightarrow {\left( p \right)^{\frac{{ - 6 + 7}}{{56}}}}{\left( q \right)^{\frac{{24 + 1}}{6}}} \\   \Rightarrow {\left( p \right)^{\frac{1}{{56}}}}{\left( q \right)^{\frac{{25}}{6}}} \\  $