How do you simplify #(0.93^6)(0.93^-8)#?

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Answer 1 · 2018-06-03T22:13:00

#=1/0.8649~~1.1562#

Since these have the same base:

#(0.93^6)(0.93^-8)#

we can use the rule for exponents:

#a^n*a^m=a^(n+m)#

#(0.93^6)(0.93^-8)=0.93^-2#

#=1/0.93^2#

#=1/0.8649~~1.1562#

Answer 2 · 2018-06-03T22:16:01

See a solution process below:

We can use this rule for exponents to begin the simplification process for the expression:

#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#(0.93^color(red)(6))(0.93^color(blue)(-8)) => 0.93^(color(red)(6) + color(blue)(-8)) => 0.93^(color(red)(6) - color(blue)(8)) => 0.93^-2#

Next, we can use this rule for exponents to eliminate the negative exponent:

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

#0.93^color(red)(-2) => 1/0.93^color(red)(- -2) => 1/0.93^color(red)(2) => 1/(0.93 xx 0.93) => 1/0.8649 => 1.1562#

#(0.93^6)(0.93^-8) ~= 1.1562#