GCSE(F), GCSE(H),

As with numeric powers, *a* x *a* = *a*^{2}, with the small 2 meaning that *a* has been multiplied by itself.

Multiplying *a*^{2} by *a* is the same as *a* x *a* x *a*, which is written as *a*^{3}.

Multiplying the same letter with different powers is carried out by adding the powers:

*a*^{3} x *a*^{4} = *a*^{(3 + 4)} = *a*^{7}.

Dividing powers is similar, with the indices being subtracted.

*a*^{5} ÷ *a*^{2}

= `frac(a^5)(a^2)`

= `frac(a times a times a times a times a )(a times a)`

= *a* x *a* x *a*

= *a*^{3}

Therefore *a*^{5} ÷ *a*^{2} = *a*^{(5 - 3)} = *a*^{3}.

*Additional and Higher:* Make sure that the correct letters carry the correct power sign:

*c*^{3}*d* x *c*^{2} = *c*^{(3 + 2)}*d* = *c*^{5}*d*.

1. Simplify *a* x *a*^{2}.

Answer: *a*^{3}

*a* x *a*^{2} = *a* x *a* x *a* = *a*^{3}

2. Simplify *y*^{7} ÷ *y*^{3}

Answer: *y*^{4}

*y*^{7} ÷ *y*^{3} = *y*^{(7 - 3)} = *y*^{4}

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