How do you simplify $(9 x^{5} y^{4}) {(3 x y^{5})}^{4}$ $(9x^5y^4)(3xy^5)^4$ leaving only positive exponents?

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Answer 1 · 2018-04-19T08:48:10

$729 x^{9} y^{24}$ $729x^9y^24$

$(9 x^{5} y^{4}) {(3 x y^{5})}^{4}$ $(9x^5y^4)color(blue)((3xy^5)^4)$

First remove the brackets.

Raise all the factors in the second bracket to the power of $4$ $4$

$= 9 x^{5} y^{4} \times 81 x^{4} y^{20}$ $=9x^5y^4 xxcolor(blue)( 81x^4y^20)$

Now simplify:
multiply the numbers and add the indices of like bases

$= 9 \times 81 x^{5 + 4} y^{4 + 20}$ $=9xx81" " x^(5+4) " "y^(4+20)$

$= 729 x^{9} y^{24}$ $= 729x^9y^24$

How do you simplify (9x5y4)(3xy5)4(9x^5y^4)(3xy^5)^4 leaving only positive exponents?