Question 430116: Rewrite & simplify the given expression using positive exponents only.
(square root x^-5 + x^-5y^7z^-2)(x^9y^-2z^9)
Only x^-5 is a square root
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! ~ = square root of in this answer
(~(x^(-5))+x^(-5)y^(7)z^(-2))(x^(9)y^(-2)z^(9))
Pull all perfect square roots out from under the radical. In this case, remove the x^(-3) because it is a perfect square.
(x^(-3)~(x)+x^(-5)y^(7)z^(-2))(x^(9)y^(-2)z^(9))
Move all negative exponents from the numerator to the denominator and make the exponents positive. A negative exponent follows the rule: a^(-n)=(1)/(a^(n)).
(x^(-3)~(x)+(y^(7))/(x^(5)z^(2)))(x^(9)y^(-2)z^(9))
Remove the negative exponent in the numerator by rewriting x^(-3)~(x) as (~(x))/(x^(3)). A negative exponent follows the rule: a^(-n)=(1)/(a^(n)).
((~(x))/(x^(3))+(y^(7))/(x^(5)z^(2)))(x^(9)y^(-2)z^(9))
To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is x^(5)z^(2). Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
((~(x))/(x^(3))*(x^(2)z^(2))/(x^(2)z^(2))+(y^(7))/(x^(5)z^(2)))(x^(9)y^(-2)z^(9))
Complete the multiplication to produce a denominator of x^(5)z^(2) in each expression.
((x^(2)z^(2)~(x))/(x^(5)z^(2))+(y^(7))/(x^(5)z^(2)))(x^(9)y^(-2)z^(9))
Combine the numerators of all expressions that have common denominators.
((x^(2)z^(2)~(x)+y^(7))/(x^(5)z^(2)))(x^(9)y^(-2)z^(9))
Remove the negative exponent in the numerator by rewriting x^(9)y^(-2)z^(9) as (x^(9)z^(9))/(y^(2)). A negative exponent follows the rule: a^(-n)=(1)/(a^(n)).
((x^(2)z^(2)~(x)+y^(7))/(x^(5)z^(2)))((x^(9)z^(9))/(y^(2)))
Multiply ((x^(2)z^(2)~(x)+y^(7)))/(x^(5)z^(2)) by (x^(9)z^(9))/(y^(2)) to get (x^(4)z^(7)(x^(2)z^(2)~(x)+y^(7)))/(y^(2)).
((x^(4)z^(7)(x^(2)z^(2)~(x)+y^(7)))/(y^(2)))
Remove the parentheses around the expression (x^(4)z^(7)(x^(2)z^(2)~(x)+y^(7)))/(y^(2)).
(x^(4)z^(7)(x^(2)z^(2)~(x)+y^(7)))/(y^(2))
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