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The expression, [tex](-243)^{-3/5}[/tex] on simplification using the laws of the exponent can be written as - (1/27).
Exponents are of the form aˣ, read as " a to the power x", function as a multiplied by itself x number of times, and are used in a numerical and algebraic expression.
To simplify these expressions, we use the following laws of the exponents:
[tex]1. a^m.a^n = a^{m + n}\\2.\frac{a^m}{a^n} = a^{m-n}\\ 3. (a^m)^n = a^{mn}\\4. a^{-m} = \frac{1}{a^m}\\5. a^0 = 1[/tex]
In the question, we are asked to simplify the expression, [tex](-243)^{-3/5}[/tex].
The expression can be solved using the laws of exponent as follows:
[tex](-243)^{-3/5}\\[/tex]
= [tex]((-3)^5)^{-3/5}[/tex]
= [tex](-3)^{-3}[/tex] {Using the law of exponent: [tex](a^m)^n = a^{mn}[/tex]}
= [tex]\frac{1}{-3^3}[/tex] {Using the law of exponent: [tex]a^{-m} = \frac{1}{a^m}[/tex]}
= 1/(-27)
= - (1/27).
Thus, the expression, [tex](-243)^{-3/5}[/tex] on simplification using the laws of exponent can be written as - (1/27).
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