Question

value of 8 power 0 in mathematics. I have doubts in powers and exponents.

Answer 1

$\large{\boxed{\tt{ {(8)}^{0} \implies 1}}}$

We have got the answer as 1 because any number raised to 0 or having the power of zero gives the product as 1. It is because if any number is raised to 0 ; it doesn't have any power and the product of a powerless number is 1 .

In case of $\tt{ {2}^{2}}$ we multiply 2 with 2 => 2 × 2 which is equal to 4. In case of $\tt{ {6}^{0}}$ there is no number to be multiplied with 6 => 6 × ? so we directly take 1 as the answer.

Important laws of indices :

• $\tt{ {(a)}^{m} \times {(a)}^{n} \implies {(a)}^{m+n}}$

• $\tt{ {(a)}^{m} \div {(a)}^{n} \implies {(a)}^{m-n}}$

• $\tt{ {(a)}^{-m} \implies \dfrac{1}{{(a)}^{m}}}$

• $\tt{ {({a}^{m})}^{n} \implies {(a)}^{m \times n}}$

• $\tt{ {ab}^{m} \implies {a}^{m} \times {b}^{m}}$

• $\tt{ {a}^{0} \implies 1}$

• $\tt{ {a}^{1} \implies a}$

The only way to remember these identities is to recollect them at least once in a day.