Math 96--Calculator and Exponent Key and Root Key--page 1

Transcription

1 Math 96--Calculator a Eponent Ke a Root Ke--page 1 Part A--Eponent Ke, using fractions. We alread know that a fraction eponent represents a radical. Sometimes when we work with a fractional eponent, the base is a perfect a factors so we actuall get a result that has no radical. For eample, a. You could also use the power chart (on the back of the multiplication table) to avoid the prime factoring. From the chart, 2 ; then 5 = 25. The eponent ke on our calculator, along with the fraction ke (a b/c), will allow ou to ke in the above problem a get 25 for an answer. In general, ou ke in the base, the eponent ke, the fractional eponent (numerator, a b/c ke, denominator), a the equal sign. On the TI30Xa, this is the eponent ke:. Some calculators use this for the eponent: ^. Other calculators use this for the eponent ke:. Look at our calculator to know what our eponent ke looks like. On the first eamples, I ll show the various was to ke in the problem, based on the various eponent kes available. b. Ke in 125,, 2, a b/c, 3, =. The displa should read 25. Ke in 125, ^, 2, a b/c, 3, =. The displa should read 25. Ke in 125,, 2, a b/c, 3, =. The displa should read 25. c. Ke in 64,, 3, a b/c, 2, =. The displa should read 512. Ke in 64, ^, 3, a b/c, 2, =. The displa should read 512. Ke in 64,, 3, a b/c, 2, =. The displa should read 512. Now ou tr these on the calculator. Use the eponent ke (, ^, or ) a the fraction ke (a b/c) Part B--The Root Ke. We also know how to simplif radicals using prime factors a the ie to count the number of identical primes to make a perfect. For eample, d. e.

2 Math 96--Calculator a Eponent Ke a Root Ke--page 2 You could also use our power chart (on the back of our multiplication table). Could we do this on the calculator? Yes! We could use the root ke. On the TI30Xa calculator, the root ke is in ellow above the eponent ke. The root ke looks like this:. On some calculators, the root ke looks like this: a is located above the ke. On the TI30Xa, here is how to use the root ke. Ke in the radica, the root ke (so ou have to press the ellow 2 button a to get to the root ke ), the ie, =. For eample, would be keed in like this: radica 32, 2 to use, ie 5, =, 2. On other calculators, here is how to use the root ke. Ke in the ie, the root ke (so ou have to press the shift ke a to get to the root ke ), the radica, =. For eample, would be keed in like this: ie 5, 2 to use, radica 32, =, 2. Pla with our calculator until ou know the kestrokes! Practice with the following eamples. f. Ke in 27, root ke, ie 3, =. The displa should read 3. Ke in 3, root ke, radica 27, =. The displa should read 3. g. Ke in 125, root ke, ie 3, =. The displa should read 5. Ke in 3, root ke, radica 125, =. The displa should read 5. h. Ke in 256, root ke, ie 4, =. The displa should read 4. Ke in 4, root ke, radica 256, =. The displa should read 4. i. Ke in 625, root ke, ie 4, =. The displa should read 5. Ke in 4, root ke, radica 625, =. The displa should read 5. Now ou tr these using the root ke on our calculator

3 Math 96--Calculator a Eponent Ke a Root Ke--page 3 Part C--Two was to work perfect radicals. You now have two was to work radicals that are perfect. One wa is to use the root ke ( or, both of which are located above the eponent ke so ou have to use the 2 button or shift button to use the root ke). The other wa would be to re-write the radical as a base a a fractional eponent. Then ou could use the eponent ke (, ^, or ) a the fraction ke (a b/c). Look at a couple of eamples, done two was. j. 512, root ke, ie 3, =. The displa should read 8. 3, root ke, radica 512, =. The displa should read 8. k. 512, eponent ke, 1, a b/c, 3, =. The displa should read 8. l. 64, root ke, ie 6, =. The displa should read 2. 6, root ke, radica 64, =. The displa should read 2. m. 64, eponent ke, 1, a b/c, 6, =. The displa should read 2. n. 961, root ke, ie 2, =. The displa should read 31. o. 961, eponent ke, 1, a b/c, 2, =. The displa should read 31. p. 961, square root ke ( ). The displa should read 31. square root ke ( ), 961, =. The displa should read 31. It s up to ou to decide whether ou d like to use the root ke or the eponent ke. If ou use the root ke, ou have to remember to ke in the radica, the root ke, the ie, a the equal sign OR to ke in the ie, the root ke, the radica a the equal sign. If ou use the eponent ke, ou need to re-write the radical using fractional eponents a then ke in the base, the eponent ke (, ^, or ), the numerator, the a b/c ke, the denominator, a the equal sign.

4 Math 96--Calculator a Eponent Ke a Root Ke--page 4 Now ou work these. Decide whether ou want to use the root ke or the eponent ke Part D--Etra Ideas. When ou get a problem like this: manuall:, we would work it like this q. r. On the calculator, we would ke in 9, (or ^ or ), 5, a b/c, 2, + to ke (or some calculators use the negative sign first a then 5, a b/c, 2), =. Look at the displa; ou get a decimal: Let s convert that to a fraction b using the fraction-to-decimal ke (F D). Fi that ke! Usuall, it s above some other ke so is accessed b using the 2 ke or the Shift ke. Now look at the displa. It should show the fraction. s. The problem with using the calculator for these problems is the TI30Xa calculator won t convert all decimals to fractions. Once the denominator of a fraction is above 999, this calculator won t convert. So, if we were working the problem, we would work manuall like this: t. If ou tr this on the calculator, ou would ke in 36, eponent ke, the negative eponent, =. Look at the displa; ou get a decimal: When ou tr to convert from a decimal to a fraction with the 2 ke a F D, nothing happens. That s because the denominator is too big! Most instructors won t accept the decimal because it isn t accurate enough. So...it is important to be able to do these manuall. The answer most instructors want is.

5 Math 96--Calculator a Eponent Ke a Root Ke--page 5 Now ou tr these. Write our answer in fraction form. The first would work with a calculator, but the seco will not so work it manuall Answer Ke or 12.