What is expand p^{1/4}(p^{3/4}+3p^{7/4}) ?

The solution to expand p^{1/4}(p^{3/4}+3p^{7/4}) is p+3p^2

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expand p^{1/4}(p^{3/4}+3p^{7/4})

expand

p^{\frac{1}{4}} (p^{\frac{3}{4}} + 3 p^{\frac{7}{4}})

p + 3 p^{2}

Solution steps

p^{\frac{1}{4}} (p^{\frac{3}{4}} + 3 p^{\frac{7}{4}})

Apply the distributive law:

a (b + c) = ab + a c

p^{\frac{1}{4}} (p^{\frac{3}{4}} + 3 p^{\frac{7}{4}}) = p^{\frac{1}{4}} p^{\frac{3}{4}} + p^{\frac{1}{4}} \cdot 3 p^{\frac{7}{4}}

= p^{\frac{1}{4}} p^{\frac{3}{4}} + p^{\frac{1}{4}} \cdot 3 p^{\frac{7}{4}}

p^{\frac{1}{4}} p^{\frac{3}{4}} = p

p^{\frac{1}{4}} \cdot 3 p^{\frac{7}{4}} = 3 p^{2}

= p + 3 p^{2}

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What is expand p^{1/4}(p^{3/4}+3p^{7/4}) ?
The solution to expand p^{1/4}(p^{3/4}+3p^{7/4}) is p+3p^2