How do you simplify #\frac { 10b ^ { 5} T ^ { 5} } { 2b ^ { - 2} T ^ { 8} }#?

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Answer 1 · 2018-01-20T23:32:13

See a solution process below:

First, rewrite the expression as:

#(10/2)(b^5/b^-2)(T^5/T^8) => 5(b^5/b^-2)(T^5/T^8)#

Next, use this rule of exponents to simplify the #b# term:

#x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))#

#5(b^color(red)(5)/b^color(blue)(-2))(T^5/T^8) => 5b^(color(red)(5)-color(blue)(-2))(T^5/T^8) => 5b^(color(red)(5)+color(blue)(2))(T^5/T^8) =>#

#5b^7(T^5/T^8)#

Now, use this rule of exponents to simplify the #T# term:

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

#5b^7(T^color(red)(5)/T^color(blue)(8)) => 5b^7 xx 1/T^(color(blue)(8)-color(red)(5)) => 5b^7 xx 1/T^3 => (5b^7)/T^3#