Questions: Evaluate the following expressions. a. 10^3 × 10^6 b. 10^5 × 10^-3 c. 10^12 / 10^4 d. 10^6 / 10^-2 (Simplify your answer. Type your answer using exponential notation.)

Solution Steps

To evaluate the given expressions, we can use the properties of exponents. Specifically, when multiplying powers with the same base, we add the exponents, and when dividing, we subtract the exponents.

a. For \(10^{3} \times 10^{6}\), add the exponents: \(3 + 6\).

b. For \(10^{5} \times 10^{-3}\), add the exponents: \(5 + (-3)\).

c. For \(\frac{10^{12}}{10^{4}}\), subtract the exponents: \(12 - 4\).

Using the property of exponents, we have: \[ 10^{3} \times 10^{6} = 10^{3 + 6} = 10^{9} \] Calculating this gives: \[ 10^{9} = 1000000000 \]

Again, applying the property of exponents: \[ 10^{5} \times 10^{-3} = 10^{5 + (-3)} = 10^{2} \] Calculating this results in: \[ 10^{2} = 100 \]

Using the division property of exponents: \[ \frac{10^{12}}{10^{4}} = 10^{12 - 4} = 10^{8} \] Calculating this gives: \[ 10^{8} = 100000000 \]

Final Answer