How do you simplify #\frac { 13x ^ { - 5} y ^ { 0} } { 5^- 3z ^- 10}#?

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Answer 1 · 2018-01-15T15:06:49

See a solution process below:

First, use this rule for exponents to simplify the #y# term:

#a^color(red)(0) = 1#

#(13x^-5y^color(red)(0))/(5^-3z^-10) => (13x^-5 * 1)/(5^-3z^-10) => (13x^-5 * 1)/(5^-3z^-10) => (13x^-5)/(5^-3z^-10)#

Next, we can eliminate the negative exponents in the denominator using this rule of exponents:

#1/x^color(red)(a) = x^color(red)(-a)#

#(13x^-5)/(5^color(red)(-3)z^color(red)(-10)) => (13x^-5)(5^color(red)(- -3)z^color(red)(- -10)) => (13x^-5)(5^color(red)(3)z^color(red)(10)) =>#

#(13x^-5)(125z^10) => (13 xx 125)(x^-5z^10) => 1625x^-5z^10#

Now, we can use this rule for exponents to eliminate the negative exponent for the #x# term:

#x^color(red)(a) = 1/x^color(red)(-a)#

#1625x^color(red)(-5)z^10 => (1625z^10)/x^color(red)(- -5) => (1625z^10)/x^5#