Question 1

Simplify the following expression using positive indices: \(5{m^{ - 4}}\)

\(\dfrac{5}{{{m^4}}}\)

Question 2

Simplify the following expression: \({\left( {\dfrac{{{x^2}}}{2}} \right)^{ - 4}}\)

\(\dfrac{{16}}{{{x^8}}}\)

Question 3

Simplify the following expression: \({\left( {\dfrac{{3a}}{{7b}}} \right)^{ - 2}}\)

\(\dfrac{{49{b^2}}}{{9{a^2}}}\)

Question 4

Simplify without negative indices  \({\left( {\dfrac{{3{m^4}}}{{5{n^3}}}} \right)^{ - 2}}\)

\(\dfrac{{25{n^6}}}{{9{m^8}}}\)

Question 5

Simplify without negative indices  \({\left( {\dfrac{{5{x^2}}}{{7{y^3}}}} \right)^{ - 3}}\)

\(\dfrac{{343{y^9}}}{{125{x^6}}}\)

Question 6

Simplify without negative indices  \({\left( {\dfrac{5}{{2{m^4}}}} \right)^{ - 2}}\)

\(\dfrac{{4{m^8}}}{{25}}\)

Question 7

Simplify using positive indices \(2p^{-3} \times p\)

\(\dfrac{2}{p^2}\)

Question 8

Simplify \(\left ( \dfrac{x^3}{3}\right )^{-2}\)

\(\dfrac{9}{x^6}\)

Question 9

Simplify \(\left( \dfrac{x^3}{3}\right )^{-3}\)

\(\dfrac{1}{27x^6}\)

Question 10

Simplify using positive indices \((\dfrac{5}{a^2})^{-2}\)

\(\dfrac{a^4}{25}\)

Question 11

Simplify using positive indices \((\dfrac{a^3}{4})^{-2}\)

\(\dfrac{16}{a^6}\)