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Simplifying expressions using the laws of indicesSimplifying indices

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.

Part of MathsNumerical skills

Simplifying indices

Watch this video to learn about the laws of 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 \({y^7} \times {y^3} \times {y^5}\)

Question

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

Question

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

Question

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

Question

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