Let's simplify each part of the question and write the answers in scientific notation:

a) $(5.1 \times 10^{-2})(2.6 \times 10^3)$

To solve this, multiply the numbers and handle the powers of 10 separately:

1. Multiply the base numbers:
   $5.1 \times 2.6 = 13.26$

2. Multiply the powers of 10:
   $10^{-2} \times 10^3 = 10^{1}$

So, the product becomes:
$13.26 \times 10^1$

Since $13.26$ is not in proper scientific notation (it should be between 1 and 10), we convert it:
$13.26 = 1.326 \times 10^1$

Therefore:
$13.26 \times 10^1 = 1.326 \times 10^2$

b) $(4.9 \times 10^{-1})(7 \times 10^{-1})$

1. Multiply the base numbers:
   $4.9 \times 7 = 34.3$

2. Multiply the powers of 10:
   $10^{-1} \times 10^{-1} = 10^{-2}$

So, the product becomes:
$34.3 \times 10^{-2}$

Again, we convert $34.3$ to scientific notation:
$34.3 = 3.43 \times 10^1$

Therefore:
$34.3 \times 10^{-2} = 3.43 \times 10^{-1}$

Final Answers:

a) $1.326 \times 10^2$
b) $3.43 \times 10^{-1}$

Would you like further details or clarifications?

Here are 5 related questions:

1. How do you multiply numbers in scientific notation?
2. Why is it important to convert the result into proper scientific notation?
3. How do you simplify powers of 10 when multiplying them?
4. Can you convert $1.326 \times 10^2$ into standard form?
5. What happens when you divide numbers in scientific notation?

Tip: When working with scientific notation, always ensure the number is between 1 and 10 before finalizing your answer.