Question

Express the following in exponential form:
$t\times t$

Answer 1

Hint: To express this in exponential form we first need to know the meaning of exponential form. After that we would write the exponential form of that number. The general exponential function has the number $e$ as its base, but here we are asked to raise a random number $t$ to the power of 2.

Complete step-by-step solution:
We say that we raise any number to a power of ‘n’ if we multiply it ‘n’ times by itself. And the power to which the number is raised is called its exponent. So, when we say we need an expression in exponential form, we need to raise the number to that power or in other words, multiply that number with itself ‘n’ number of times. The number which is raised to the exponent is called the Base.
For example, if we multiply 2 six times i.e.
$2\times 2\times 2 \times 2\times 2\times 2$
Then we can write it as $2^5$
And in this case, 2 is the base and 5 is the exponent, the power to which it is raised.
Here, we are given$t\times t$, which is t squared or $t^2$
So, we can say that the exponential form of $t\times t$ is $t^2$.

Note: Also note that it has not asked to use decimal exponent, so do not try to include the power of 10’s here. Moreover, if the number of times the variable has been multiplied is large enough then make groups of five and then collect them to ensure that the result produced is not invalid.