The image you uploaded contains multiple exponential expressions and problems related to simplifying them using the laws of exponents.

Let's break down each problem from the image:

Simplifying and expressing in exponential form:

1. (i) $32 \times 34 \times 38$:
   Combine the terms with the same base using exponent rules.

2. (ii) $615 \div 610$:
   This is simplifying a division of numbers with powers of 10.

3. (iii) $a^2 \times a^2$:
   Use the property of exponents: $a^m \times a^n = a^{m+n}$.

4. (iv) $7 \times 7^2$:
   Apply the same exponent law as above.

5. (v) $(5^2)^3 \div 5^4$:
   Apply the law of exponents for powers of powers: $(a^m)^n = a^{m \times n}$.

6. (vi) $25^x \times 5^5$:
   Convert $25$ as a power of $5$ and then simplify.

7. (vii) $8^1 \times 8^2$:
   Apply the product rule for exponents.

8. (viii) $(3^4)^3$:
   Simplify using the exponent rule for powers of powers.

9. (ix) $(2^{20} + 2^{15}) \times 2^{23}$:
   Simplify using the rule for adding and subtracting exponents.

Additional Problems:

• (ii) $\frac{3^2 \times 3^4 \times 4}{3^3 \times 3^2}$:
  Simplify using the laws of exponents on each term.

• (iii) $3^3 \times 7^2 \times 11^8$:
  Apply the rules of exponents to combine like bases.

True or False questions:

1. (i) $10^{10} \times 10^{11} = 100^{11}$
   Use the exponent multiplication rule: $a^m \times a^n = a^{m+n}$.

2. (ii) $2^3 > 5^2$
   Compare the values of both sides.

3. (iii) $3^0 = (1000)^0$
   Evaluate both sides based on the property that any non-zero number raised to the power of 0 is 1.

4. (iv) $3^0 = (1000)^0$
   Similar to (iii), use the same exponent rule.

5. (v) $2^3 \times 3^2 = 6^5$
   This will require comparison of both sides based on exponent properties.

Would you like me to solve and explain each of these step-by-step in more detail? Or do you have a specific question from this set? Let me know!

Related Questions:

1. How do you apply the rule for multiplying exponents with the same base?
2. What happens when you divide two terms with the same base raised to different powers?
3. Can you simplify expressions like $(a^m)^n$?
4. What does it mean when a number is raised to the power of 0?
5. How can we compare exponents like $2^3$ and $5^2$?

Tip: Always start by simplifying terms with the same base before dealing with mixed terms to make it easier to handle!