Question

give the answer fast it is very urgent And explain every method step by step ​

Answer 1

Question :

Write the power of the term (-6) in :

$\tt{ {(-6)}^{8} ÷ {(-6)}^{3} = {(-6)}^{?}}$

Answer :

If we carefully observe ; the given problem is in the form of the law of indices : $\tt{ {a}^{m} ÷ {a}^{n} \implies {a}^{m-n}}$ . Where in this case (a) is (-6) and (m) is (8) and (n) is (3).

So , using the same identity ; we will solve the given problem.

$\tt{ {a}^{m} ÷ {a}^{n} \implies {a}^{m-n}}$

$\tt{ {(-6)}^{8} ÷ {(-6)}^{3} \implies {(-6)}^{8 - 3}}$

$\tt{ {(-6)}^{8} ÷ {(-6)}^{3} \implies {(-6)}^{5}}$

So , the answer is : $\large{\boxed{\tt{ {(-6)}^{5}}}}$

$\tt{ {(-6)}^{5}}$ when further simplified gives us the number -7776.

More laws of indices :

• $\tt{ {a}^{m} + {a}^{n} \implies {a}^{m+n}}$
• $\tt{ {a}^{-m} \implies \dfrac{1}{m}}$
• $\tt{ {a}^{m} ÷ {a}^{n} \implies {a}^{m-n}}$
• $\tt{ {({a}^{m})}^{n} \implies {a}^{m \times n}}$
• $\tt{ {ab}^{m} \implies {a}^{m} \times {b}^{m}}$
• $\tt{ {a}^{0} \implies 1}$
• $\tt{ {a}^{1} \implies a}$