Question

Solve the expression \[{\left( {{3^{ - 1}} + {4^{ - 1}} + {5^{ - 1}}} \right)^0}\]

Answer 1

Hint: A very simple concept is used here. We all know that if the power of any number is zero then what would be the answer. It does not matter whether the number is a fraction of a whole number. This holds true for all the numbers. Here in this question power $ - 1$ is given just to confuse you.

Complete step-by-step solution:
In the given question, we have
$ = \,{\left( {{3^{ - 1}} + {4^{ - 1}} + {5^{ - 1}}} \right)^0}$
Now, we can also write
$ = {\left( {\dfrac{1}{3} + \dfrac{1}{4} + \dfrac{1}{5}} \right)^0}$
The sum of these positive numbers is a positive number and any number with zero power gives the result as $1\,.$
Hence, our required answer is $1$.
Additional information: zero to the power zero, denoted by ${0^0}$, is a mathematical expression with no agreed-upon value. The most common possibilities are $1$ or leaving the expression undefined, with justifications existing for each, depending on context. In algebra and combinatorics, the generally agreed-upon value is ${0^0} = 1$, whereas, in mathematical analysis, the expression is sometimes left undefined. Computer programming languages and software also have different ways of handling this expression.

Note: There are lots of different ways to think about it, but here’s one. Let’s go back and think about what power means. When we raise a number to the nth power, that really means that we multiply that number by itself n times, so for example, ${2^2} = 2 \times 2 = 4$. So when we raise a number to the zeroth power, that means we multiply the number by itself zero times – but that means we’re not multiplying at all.