Question

What is $a({{a}^{n-1}})$?

Answer 1

Hint: In the above question we have to deduce the value of $a({{a}^{n-1}})$. Here we see that this is the multiplication of two terms that is ${{a}^{1}}\text{ and }{{a}^{n-1}}$. As we know from law of exponent when we multiply two term whose base is same the exponent is added, mathematically we can write $\left( {{x}^{m}} \right)\left( {{x}^{p}} \right)={{x}^{m+p}}$, here $x$is the base and $m,p$ are the exponents. In the given question we have $x=a$and $m=1,p=n-1$, so we have to put all the values and solve it in order to get the solution.

Complete step by step answer:
Let us assume that
$X=a\left( {{a}^{n-1}} \right)$
Here we use the law of exponent that is the formula $\left( {{x}^{m}} \right)\left( {{x}^{p}} \right)={{x}^{m+p}}$.
We have $x=a$and $m=1,p=n-1$, so we can write
$X={{a}^{1+n-1}}$
In the above we see that sum of plus one and minus one is zero, so we can write further
$X={{a}^{n}}$
Hence $a({{a}^{n-1}})$is ${{a}^{n}}$.

Note:
It should be noted here that an exponent refers to the number of times a number is multiplied by itself. The exponent is usually shown as superscript to the right of the base. In that case, ${{a}^{n}}$is called “a raised to the ${{n}^{th}}$power”.
Some important rule of exponent
Rule1. When multiplying like bases, keep the base same and add the exponent.
Rule2: When raising a base with a power to another power, keep the base the same and multiply the exponents.
Rule3: When dividing the base, keep the base same and subtract the denominator exponent from the numerator exponent.
Rule4: When raising a product to a power, distribute the power to each factor.
Rule5: Anything raised to the zero power is one.