Question

What is one fifth to the fifth power?

Answer 1

Hint: First we need to convert the given word problem into algebraic expression. That is an algebraic expression in mathematics is an expression which is made up of variables and constants along with algebraic operations. An expression is a group of terms. Here algebraic operations are addition, subtraction, division and multiplication etc. After obtaining the algebraic expression we can simplify.

Complete step by step solution:
We have one fifth to the fifth power
That is one fifth means 1 is divided by 5 \[ =\dfrac{1}{5}\].
One fifth to the fifth power means \[ {\left( {\dfrac{1}{5}} \right)^5}\]
Then we have,
\[ \Rightarrow \dfrac{{{1^5}}}{{{5^5}}}\]
We know that 1 to the any power is one only and \[{5^5} = 3125\]
\[ \Rightarrow \dfrac{1}{{3125}}\]. This is the exact form.
\[ \Rightarrow 0.00032\]. This is the decimal form.

Note:
Algebra helps in converting a mathematical statement into an equation. We know if we have ‘more’ or ‘sum’ in the given sentence we use addition operation\[( + )\]. Similarly If we have ‘less’ or ‘difference’ we use subtraction \[( - )\]. If we have ‘quotients’ we use division operation \[( \div )\]. To define more generalized terms; we use algebra. It is a very vast branch of mathematics and is used in all the branches of mathematics like polynomial, linear equations, graphs, etc. and in daily life too.