Transcription of Negative and fractional powers - Mathematics resources
1 Negative and fractional powersmc-indices2-2009-1In many calculations you will need to use Negative and fractional powers . These are explained onthis powersNegative powers are interpreted as follows:a m=1amor equivalentlyam=1a mExamples3 2=132,15 2= 52,x 1=1x1=1x,x 2=1x2,2 5=125 Exercises1. Write the following using only positive powers :(a)1x 6, (b)x 12, (c)t 3, (d)14 3,(e)5 Without using a calculator evaluate (a)2 3,(b)3 2,(c)14 2, (d)12 5, (e)14 powersTo understand fractional powers you first need to have an understanding of roots, and in particularsquare roots and cube a number is raised to a fractional power this is interpreted as follows:a1/n=n aSo,a1/2is a square root ofaa1/3is the cube root ofaa1/4is a fourth root ofaExamples31/2=2 3,271/3=3 27or3,321/5=5 32 = 2,641/3=3 64 = 4,811/4=4 81 = mathcentre 2009 fractional powers are useful when we need to calculate rootsusing a scientific calculator.
2 Forexample to find7 38we rewrite this as381/7which can be evaluated using a scientific may need to check your calculator manual to find the precise way of doing this, probably withthe buttonsxyorx1 that you are using your calculator correctly by confirming that381/7= (4 dp)More generally we can write:am/n=n amor equivalently(n a)mExamples82/3= (3 8)2= 22= 4,and323/5= (5 32)3= 23= 8 Alternatively,82/3=3 82=3 64 = 4,and323/5=5 323=5 32768 = 8 Exercises3. Use a calculator to find, correct to 4 decimal places, a)5 96, b)4 Without using a calculator, evaluate a)43/2, b)272 Use the ruleanam=an mwithn= 0to prove thata m= Each of the following expressions can be written asan.
3 Determinenin each case:(a)1a5(b) a 1a2,(c) 1 (d)1 (a)x6, (b)1x12, (c)1t3, (d)43, (e) (a)2 3=123=18, (b)19, (c)16, (d) 32, (e) a) , b) 4. a)43/2= 8, b)272/3= (a) 5(b) 32(c) 0(d) mathcentre 2009
