Basic Math Skills : Multiplying Fractional Exponents
(Learn the mathematical process) учите математический процесс (for multiplying fractional exponents) умножения дробных чисел.
To multiply fractional exponents, change the fraction to the square root of the whole number and multiply as you would multiply fractions.
(Now I'm going to show you how) сейчас я собираюсь показать вам, (to multiply fractional exponents) как умножать дроби.
Let's take the number nine raised to the one half multiplied by sixty four raised to the one third.
The exponent of one half represents square root, and the square root of nine is three.
The exponent of one third represents the cube root, and the cube root of sixty four is four, because four times four times four is sixty four.
So, the problem is now reduced to three times four equals twelve.
This can be shown to be true because to reverse the operation we square it, so three squared equals nine which checks out. Four cubed is four times four times four is sixty four.
So, this shows that our method is correct, and the answer to this problem with fractional exponents is twelve.
Now, I'm going to show you how to multiply numbers with fractional exponents with improper fractions.
Let's take nine to the one half and multiply that by eight to the three half.
Now, three halfs is the same as one point five, which is the same as eight times itself one and a half times.
So, eight to the three halfs equals eight to the one point five, which is equal to eight times four, because it's eight times itself once and times half of itself again; that's thirty two.
So, eight to the three halfs is thirty two.
Nine to the half is three, because three is the square root of nine.
This is how you multiply numbers with fractional exponents with one of them being improper.
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