I see that you've uploaded an image of a math exam. I'll help you break down and solve the problems visible in the image. Let's go through them one by one.

Problem 21:

Simplify and write the answer in exponential form.

The expression given seems to be: $(5^2 \times x^2 \times y^2) / (5^2 \times x \times y)$

Solution:

We can simplify this by canceling out common terms in the numerator and the denominator.

1. The $5^2$ terms cancel out.
2. The $x^2 / x = x$, because $x^2 = x \cdot x$, so one $x$ cancels.
3. The $y^2 / y = y$, because $y^2 = y \cdot y$, so one $y$ cancels.

Thus, the simplified expression is: $x \times y$

Problem 22:

Solve:

The expression appears to be: $(-3) \times (-4) \times (-5) \times (-2)$

Solution:

When multiplying multiple negative numbers:

• $(-3) \times (-4) = 12$,
• $12 \times (-5) = -60$,
• $-60 \times (-2) = 120$.

So, the final result is: $120$

Problem 23:

Simplify and express in exponential form:

This looks like: $(2^2) \times 2^3 \times 2^0$

Solution:

Using the rules of exponents:

• $2^2 = 4$,
• $2^3 = 8$,
• $2^0 = 1$ (since anything raised to the power of 0 is 1).

Now, multiply these: $4 \times 8 \times 1 = 32$ This can also be written as: $2^5$

So, the exponential form is: $2^5$

The second part of the question (b) asks you to find the value of $z^2 - 3z$ when $z = 10$. Let's solve this: $z^2 - 3z = 10^2 - 3(10) = 100 - 30 = 70$

Problem 24:

Simplify using BODMAS:

The expression given seems to be: $36 - [(18 - 1)4 - (3 - 4 \times 2)]$

Solution:

Apply the BODMAS rule (Brackets, Orders, Division and Multiplication, Addition and Subtraction):

1. Inside the first bracket, solve the parentheses: $(18 - 1) = 17$ So the expression becomes: $36 - [17 \times 4 - (3 - 4 \times 2)]$
2. Inside the second bracket, solve $4 \times 2 = 8$, so: $36 - [17 \times 4 - (3 - 8)]$
3. Now, $3 - 8 = -5$, so: [ 36 - [17 \times 4 - (-5)] = 36 - [68 + 5] = 36 - 73 = -37 ]

So the final result is: $-37$

Problem 25:

Find the root of the following:

a) Solve $5p + 2 = 17$.

Solution:

Subtract 2 from both sides: $5p = 17 - 2 = 15$ Now, divide by 5: $p = 15 / 5 = 3$

b) Solve $3m - 14 = 6$.

Solution:

Add 14 to both sides: $3m = 6 + 14 = 20$ Now, divide by 3: $m = 20 / 3 = \frac{20}{3}$

If you would like further details or have any questions, feel free to ask! Here are some related questions for practice:

1. How do you simplify expressions with exponents in general?
2. What are the rules for multiplying and dividing terms with exponents?
3. How can you quickly solve linear equations with multiple variables?
4. What steps should you follow when applying the BODMAS rule?
5. How can you check your answers when solving for unknowns in an equation?

Tip: When simplifying exponents, always group terms with the same base to simplify calculations!