Question 126529
Let's say you had the expression



{{{(x^(1/2)*x^(3/2))/x^(3/4)}}} (note: the top two exponents from left to right are {{{1/2}}} and {{{3/2}}}




Now let's simplify:




{{{(x^(1/2)*x^(3/2))/x^(3/4)}}} Start with the given expression



{{{(x^(1/2+3/2))/x^(3/4)}}} Multiply the numerators by adding the exponents



{{{(x^2)/x^(3/4)}}} Add the exponents {{{1/2}}} and {{{3/2}}} to get {{{1/2+3/2=(1+3)/2=4/2=2}}}



{{{x^(2-3/4)}}} Divide the expression by subtracting the exponents



{{{x^(5/4)}}} Subtract the exponents {{{3/4}}} from {{{2}}} to get {{{2-3/4=8/4-3/4=(8-3)/4=5/4}}}




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Answer:


So {{{(x^(1/2)*x^(3/2))/x^(3/4)}}} simplifies to {{{x^(5/4)}}} (this says x to the fraction power {{{5/4}}})




In other words, {{{(x^(1/2)*x^(3/2))/x^(3/4)=x^(5/4)}}}