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Properties of Nth roots and fractional powers

It all works because $a^b \times a^c=a^{b+c}$ and $(a^b)^c=a^{b \times c}$ at least for positive $a$. So in your examples: $\sqrt[5]{\sqrt[2]{x}} = (x^{1/2})^{1/5}=x^{1/10}=\sqrt[10]{x}$ $(\sqrt[10]{...
Henry's user avatar
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Simple question regarding fraction to ratio conversions

The context matters. If I have a mixture that is 1 part of material A and 3 parts material B, then the ratio of material A to B is $1:3,$ but the fraction of material A to the whole mixture is $1:4.$ ...
Sean Roberson's user avatar
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Simple question regarding fraction to ratio conversions

They are correct answers to different questions. You did not specify the question being asked. If you are making salad dressing with four parts vinegar to eight parts oil you are using $\frac 48 =\...
Ross Millikan's user avatar
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How to combine divisions and fractions?

The expression 1÷(1/2) is different from 1÷1÷2 because of how it was written. The first expression is 1 divided by the quotient of 1 and 2, while the second expression is the quotient of 1 and 1 being ...
Adrianne Requierme's user avatar

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