Question

How do you write “$5$(times) $\times$(times) $\times$ (times) $\times$ (times) $\times$ (times) $x$” in the exponential form?

Answer 1

Firstly, read the question carefully. Then, recall the definition for the exponential form. Divide the given expression into two. Firstly, form expressions for the first half i.e., (times) $\times$(times) $\times$ (times) $\times$ (times) $\times$ (times) $x$ and then multiply the term with five.

Complete step by step solution:
We have to write the expression in exponential form. Firstly, reviving the expression for the exponential form. The exponential form is expressed as $f\left( x \right) = {a^x}$ where $a > 0$ and $a$ is not equal to $1$ and $x$ is a variable.
Going back to the question, according to the definition of the power of a natural exponent we have:
${a^x} = a \times a \times a \times \ldots \ldots \times a$
With factor $a$ repeated $x$ times.
Reading the expression given in the question from back:
Which says $x$ is multiplied with itself $5$ times, so converting this equation into mathematical expression,
$x \times x \times x \times x \times x$
Writing In the natural exponent
${x^5}$ $\ldots \left( 1 \right)$
Now reading the whole expression: “$5$(times) $\times$(times) $\times$ (times) $\times$ (times) $\times$ (times) $x$”
Multiplying the $\left( 1 \right)$ by $5$
$\Rightarrow 5{x^5}$
This is our required answer.

Note: The exponential curve grows or decays depends on the exponential function. Any quantity that grows or decays by a fixed per cent at regular intervals should possess either exponential growth or exponential decay.