Explanation: Zero Exponent So far we have looked at powers of 10 with exponents greater than 0.
What would happen to our patterns if we included 0 as a possible exponent?

1. Write 10^12 × 10^0 with a power of 10 with a single exponent using the appropriate exponent rule. Explain or show your reasoning.

A. What number could you multiply 10^12 by to get this same answer?​

1) We can use the following property to simplify the product of powers as follows:

, , (1)

Therefore, we have the following result:

A) must be multiplied either by or by to get the same answer.

Step-by-step explanation:

1) We can use the following property to simplify the product of powers as follows:

, , (1)

Therefore, we have the following result:

A) In addition, we can use this property:

, ,

We can apply the property mentioned above:

In consequence, we conclude that . must be multiplied either by or by to get the same answer.

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.