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How do you simplify $x^{\frac{2}{3}} (x^{\frac{1}{4}} - x)$ $x^(2/3)(x^(1/4) - x)$ ?

1 Answer

MathFact-orials.blogspot.com

Jun 1, 2017

$x^{\frac{11}{12}} - x^{\frac{5}{3}}$ $x^(11/12)-x^(5/3)$

Explanation:

We can distribute the $x^{\frac{2}{3}}$ $x^(2/3)$ term across the bracketed terms:

$x^{\frac{2}{3}} (x^{\frac{1}{4}} - x)$ $x^(2/3)(x^(1/4)-x)$

$x^{\frac{2}{3}} \times x^{\frac{1}{4}} - x^{\frac{2}{3}} \times x$ $x^(2/3)xxx^(1/4)-x^(2/3)xxx$

Let's first note that $x = x^{1}$ $x=x^1$

$x^{\frac{2}{3}} \times x^{\frac{1}{4}} - x^{\frac{2}{3}} \times x^{1}$ $x^(2/3)xxx^(1/4)-x^(2/3)xxx^1$

Let's also remember that when multiplying numbers with the same base, we add exponents, i.e. $x^{a} \times x^{b} = x^{a + b}$ $x^a xx x^b = x^(a+b)$ :

$x^{\frac{2}{3} + \frac{1}{4}} - x^{\frac{2}{3} + 1}$ $x^(2/3+1/4)-x^(2/3+1)$

And now we combine fractions the way we always do (i.e. make the denominators the same)

$x^{\frac{2}{3} (\frac{4}{4}) + \frac{1}{4} (\frac{3}{3})} - x^{\frac{2}{3} + 1 (\frac{3}{3})}$ $x^(2/3(4/4)+1/4(3/3))-x^(2/3+1(3/3))$

$x^{\frac{8}{12} + \frac{3}{12}} - x^{\frac{2}{3} + \frac{3}{3}}$ $x^(8/12+3/12)-x^(2/3+3/3)$

$x^{\frac{11}{12}} - x^{\frac{5}{3}}$ $x^(11/12)-x^(5/3)$

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