It as much as necessary and try to figure More examples of this, just so you make sure 4 to the 1/2 is equal toĢ, 2 squared is equal to 4. Have also written that 4 is equal to 2 squared. This starts to work out, well remember, we could Them, times each other, that same number,Ĭourse equal to 2. Two of those numbers and I were to multiply Multiply it by itself, or if I were to have Neat and elegant properties when you start manipulating Is defined this way, is it has all sorts of And we'll talk in theįuture about why this is, and the reason why this Is that 4 to the 1/2 power is the exact same thingĪs the square root of 4. That most people use, or in fact that all people use here, So, the mathematicalĬonvention here, the mathematical definition To pause the video and at least take a guessĪbout what you think this is. Now let's think aboutįractional exponents. And we already knowĤ to the third is 64, so this is going to be 1/64. Tells us to take the reciprocal 1/4 to the third. So for example, if I were takeĤ to the negative 3 power, we know this negative
We also know a little bitĪbout negative exponents. Going to result in 4 times 4 is 16, times 4 is 64. Or you can also view itĪs starting with a 1, and then multiplying the 1īy 4, or multiplying that by 4, three times. To taking three fours and multiplying them. If it gets rounded to 0.3, the exponent would then be 3/10 which means do the 10th root, then cube the result.īit about exponents. If you convert it to decimal form: 1/3 = 0.33333.
For example: An exponent of 1/3 = Do a cube root. If you happen to do this, then you have changed the exponent. There is also the risk that you convert a fraction to decimal, find it repeats and you then round the decimal value. You would have to convert to a fraction to make the info visible. If the exponent is in decimal form, that information is not visible. If you have a problem like: (-8)^(2/3) you can see that you need to do a cube root (the 3 in the denominator) and then square the result (the 2 in the numerator. It it is 4, then the problem is working with a 4throot. If the denominato is 3, then the problem is working with a cube root. You have a denominator of 2, so it indicates a square root. The denominator of the fraction tells you the radical index. However, the fraction form is easier to understand.
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