Indices

Simplifying indices

The two basic laws of indices are:

{a^m} \times {a^n} = {a^{m + n}}

{a^m} \div {a^n} = {a^{m - n}}

Try to use these to work through the example questions below.

Question

Simplify {y^7} \times {y^3} \times {y^5}

Use the multiplication law. This tells you to add the indices.

= {y^{7 + 3 + 5}} = {y^{15}}

Question

Simplify {y^{10}} \div {y^3}

This could also have been written as:

\frac{{{y^{10}}}}{{{y^3}}}

Use the division law which tells you to subtract the indices.

= {y^{10 - 3}} = {y^7}

Question

Simplify \frac{{{y^7} \times {y^4}}}{{{y^5}}}

= \frac{{{y^{7 + 4}}}}{{{y^5}}}

Use the multiplication law, add the numerator indices.

= \frac{{{y^{11}}}}{{{y^5}}}

Use the division law, subtract the indices.

= {y^{11 - 5}} = {y^6}

Question

Simplify y \times {y^8} \times {y^4}

y \times {y^8} \times {y^4}

=y^{1+8+4}

Remember y = {y^1}

=y^{13}

Question

Simplify {y^6} \times {y^0}

= {y^{6 + 0}} = {y^6}

This shows that {y^0} = 1