Question

Represent the following expressions as a power of the number a where a ≠ 0. ((a ) ) ÷(a ÷a ) (a · a · a )÷(a ÷a ) a ·(a ) ÷a 164 - 2 - 1 - 1 - 1 2

Answer 1

To represent the given expressions as powers of the number a, we can use the rules of exponents to simplify each expression.

Step-by-step explanation:

To represent the given expressions as powers of the number a, we need to simplify each expression. Let's go through them step by step:

1. (((a)n) ÷ (a ÷a)) = (an) × (a ÷a)-1 = an × a-1 = an + -1 = an-1
2. (a · a · a ) ÷ (a ÷a ) = (a3) ÷ (a1) = a3-1 = a2
3. a · (a ) ÷ a = a1 · (a1) ÷ a1 = (a1 · a1) ÷ a1 = a1 + 1 - 1 = a1
4. 164 - 2 - 1 - 1 - 1 2 = 162 - 21 - 11 - 11 - 12 = 16 - 2 - 1 - 1 - 4 = 8 - 2 - 1 - 4 = 6 - 1 - 4 = 5 - 4 = 1