Question

What is $3$ to the $8^{th}$ power?

Answer 1

Hint: The above question is related to the bases and exponents. In the above question, we have been given the base equal to three, whose eighth power needs to be calculated. Firstly, we need to write a mathematical expression for the given statement. The power of a number is written as a superscript to the right of the number. So the mathematical expression for the given statement will be written as ${{3}^{8}}$. The power of a base indicates the number of times the base is being multiplied with itself. Thus, we have to multiply three eight times by itself to obtain the final answer.

Complete step by step answer:
According to the question, we have to calculate the value of three to the eighth power. This mathematical expression for this statement can be written as
$\Rightarrow {{3}^{8}}$
Now, we know that the power over a number indicates the number of times it is being multiplied with itself. Therefore, we can expand the above expression as
$\Rightarrow 3\times 3\times 3\times 3\times 3\times 3\times 3\times 3$
On solving the above expression, we finally get
$\Rightarrow 6561$

Hence, the value of three to the eighth power is equal to $6561$.

Note: We can put $8=4\times 2$ in the expression ${{3}^{8}}$ to get ${{3}^{4\times 2}}$ and use the property of the multiplication of the exponents to write it as ${{\left( {{3}^{4}} \right)}^{2}}$. The value of ${{3}^{4}}$ can be easily obtained to be equal to $81$ so that the expression reduces to ${{81}^{2}}$ which can be solved by using the algebraic identity ${{\left( a+b \right)}^{2}}={{a}^{2}}+2ab+{{b}^{2}}$ by substituting $a=80$ and $b=1$.