Question

How does one simplify $ - {243^{ - \dfrac{4}{5}}}$ ?

Answer 1

Hint: For solving this particular question , we have to express the given number into its equivalent exponential form , then simplify the expression by using algebraic identities and by performing arithmetic operations such as addition , subtraction , multiplication, and division . We have to convert numbers into its equivalent exponential form where required.

Complete step-by-step solution:
We have to simplify the given expression that is $ - {243^{ - \dfrac{4}{5}}}$ ,
Now, we can express $ - 243$ in the exponent form as ,
$ \Rightarrow {\left( { - 3} \right)^{5 \times - \dfrac{4}{5}}}$
Now , simplify the above expression ,
We will get ,
$ \Rightarrow {\left( { - 3} \right)^{ - 4}}$
Now using the identity which stated as ${x^{ - a}} = {\left( {\dfrac{1}{x}} \right)^a}$ ,
We will get as follow by applying the above identity,
$ \Rightarrow {\left( { - \dfrac{1}{3}} \right)^4}$
$ \Rightarrow \dfrac{{{{( - 1)}^4}}}{{{{(3)}^4}}}$
$ \Rightarrow \dfrac{1}{{81}}$
$ \Rightarrow 0.012345$
Here, we get the required answer.

Note: Before you evaluate an algebraic expression as given the question , your aim is to simplify it as much as possible . Simplifying an expression can make all of your calculations much easier and simpler. Here we are having some of the fundamental steps needed to simplify an algebraic expression: Step I. Always try to remove the parentheses given in the expression by multiplying with its corresponding factors. Step II. Simplify the given expression by using exponent rules to get rid of parentheses in terms of exponents. Step III. Try to make it less complex by combining like terms , do operations on like terms first in order to combine them. Step IV. Lastly try to combine all the constant by doing so you will get you desired result