Let's break down the math problems visible in the image.

1. First Question (Exponent Laws):

You are asked to determine the correct statements among four expressions involving exponents.

• Expression 1: $m^3 \times m^5 = m^8$

  • This is correct, as $m^a \times m^b = m^{a+b}$.

• Expression 2: $7^7 \times 7^2 = 7^8$

  • This is incorrect because it should be $7^{7+2} = 7^9$.

• Expression 3: $x^n \times x^4 = x^{n^2}$

  • This is incorrect, because $x^n \times x^4 = x^{n+4}$, not $x^{n^2}$.

• Expression 4: $n^8 \times n^4 = n^{32}$

  • This is incorrect. It should be $n^{8+4} = n^{12}$, not $n^{32}$.

Thus, the correct answer is 1) dan 2), which matches option A.

2. Second Question (Exponent Expressions):

In this question, you need to check which statements about exponents are correct.

• Statement 1: $\frac{4^3}{4^2} = 4$

  • This is correct, as $\frac{4^3}{4^2} = 4^{3-2} = 4^1 = 4$.

• Statement 2: $\frac{(-4)^7}{(-4)^2} = (-4)^5$

  • This is correct, as $\frac{(-4)^7}{(-4)^2} = (-4)^{7-2} = (-4)^5$.

• Statement 3: $\frac{x}{x^2} = x^7$

  • This is incorrect. Simplifying $\frac{x}{x^2}$, you get $x^{1-2} = x^{-1}$, not $x^7$.

• Statement 4: $\frac{y^{10}}{y^8} = y^{12}$

  • This is incorrect. It should be $y^{10-8} = y^2$, not $y^{12}$.

Thus, the correct statements are 1) dan 2), which corresponds to option A.

3. Third Question (Surface Area and Volume of a Cube):

The side length of the cube is given as $3t$. You are asked to find the ratio of the surface area to the volume.

• The surface area of a cube with side length $s$ is $6s^2$, so with side length $3t$, the surface area is: $6(3t)^2 = 6 \times 9t^2 = 54t^2$

• The volume of a cube with side length $s$ is $s^3$, so the volume is: $(3t)^3 = 27t^3$

Thus, the ratio of surface area to volume is: $\frac{54t^2}{27t^3} = \frac{54}{27} \times \frac{1}{t} = 2:t$

The correct answer is option A: 2 : t.

Would you like any detailed explanation or have further questions?

5 Relative Questions:

1. What are the general laws of exponents for division?
2. How do you find the surface area of a rectangular prism?
3. What is the relationship between exponentiation and logarithms?
4. Can exponents be negative? If so, how are they interpreted?
5. How do you calculate the volume of irregular shapes compared to cubes?

Tip:

When simplifying expressions with exponents, always apply the basic exponent rules: multiplication means adding exponents, and division means subtracting them.