Indices show where a number has been multiplied by itself, eg squared or cubed, or to show roots of numbers, eg square root. Some terms with indices can be simplified using the laws of indices.

Simplify \({y^2} \times {y^7}\)

\[{y^{14}}\]

\[{y^{9}}\]

\[{y^{ - 5}}\]

Simplify \({y^9} \div {y^3}\)

\[{y^3}\]

\[{y^{ - 6}}\]

\[{y^6}\]

Simplify \(\frac{{{y^6} \times {y^7}}}{{{y^3}}}\)

\[{y^9}\]

\[{y^{10}}\]

Simplify \({y^2} \div {y^3}\)

\[\frac{1}{y}\]

\[y\]

\[{y^{\frac{2}{3}}}\]

Simplify \(3{m^{ - 2}} \times 6{m^{ - 2}}\)

\[18{m^{ - 4}}\]

\[18\]

\[18{m^4}\]

Evaluate \({8^{\frac{2}{3}}}\)

\[4\]

\[16\]

\[32\]

How can you simplify \(\frac{(d^{3} \times d^{4})}{d^{5}}\)?

d^{9}

3d^{2}

d^{2}

What is (e^{3})^{4} simplified?

4e^{12}

e^{7}

e^{12}

What is 6^{-2} simplified?

-12

\[\frac{1}{36}\]

36

What is \(81 ^\frac{1}{2}\) simplified?

9

40.5

-4.5