Powers


Start off by going to Key Skills


Introduction


I will just state a few points

any number to the power zero is one, e.g.

70=1,    30=1,    120=1,     x0=1    


Remember also that

7 = 71,    3= 31,    etc.


Multiplying and Dividing Numbers with Indices


If I can state a couple of rules by example

73 × 72= 7(3+2)= 75

75 ÷ 72= 7(5-2) = 73


To see how these rules work, consider the 'long method' in each case.

73 × 72= (7 × 7× 7) × (7× 7) =75

and

75 ÷ 72= (7 × 7× 7× 7× 7) ÷ (7× 7) = 73


These rules can be generalized to more complicated problems, for example

\[ \frac{7^5 \times 7^2}{7^3} \] \[ = \frac{7^7}{7^3} \] \[ =7^4 \]