How do you simplify #(-15x^-5y^-5)/(-3x^7y^-10)# without negative exponents?

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Answer 1 · 2016-09-13T18:22:46

#(5y^5)/x^12#

Let's get rid of the negative indices first.

Recall: #x^-m = 1/x^m " "and" " 1/x^-m = x^m #

#(-15x^-5y^-5)/(-3x^7y^-10)#

=#(-15y^10)/(-3x^7x^5y^5)" "larr# no negative indices - now simplify

To simplify, you need to:

=#(5y^5)/x^12#

Answer 2 · 2016-09-13T18:29:55

A negative exponent basically means to divide. To remove the negative exponents write the problem as a complex fraction.

# x^-5# = # 1/ x^5#

# y^-5# = # 1/ y^5#

so the numerator of the this fraction can be written as a division problem

# -15/( x^5 xx y^5)#

# y^-10# = # 1/ y^10 #

so the denominator of the fraction can be written as a division problem

#( -3 xx x^7)/ ( y^10) #

Now put the two complex fractions together and this gives.

#(-15) / ( x^5 xx y^5)/(-3 xx x^7)/ (y^10)#

Now multiple the denominator by its reciprocal and #
also multiple the numerator by the same reciprocal

# (-15)/ (x^5 xx y^5) xx (y^10)/(-3 xx x^7) #

This gives # (+5) xx (y^5) /(x^12) #

This is the answer because the denominator times its reciprocal equals 1