I'll solve the mathematical problems visible in the uploaded image. Let’s address the problems one by one.

1. Приведите одночлен к стандартному виду и подчеркните коэффициент:

a) $8x^3c$

Already in standard form. Coefficient = 8.

b) $3a \cdot (-0.5b) \cdot 4c$

Simplify:
$3a \cdot (-0.5b) \cdot 4c = -6abc$
Coefficient = -6.

c) $4a \cdot 2ae$

Simplify:
$4a \cdot 2ae = 8a^2e$
Coefficient = 8.

2. Выполните умножение:

a) $0.4a^3b^5 \cdot 1.5a^3b$

Simplify:
$(0.4 \cdot 1.5)a^{3+3}b^{5+1} = 0.6a^6b^6$

b) $-2.8b^3c^7 \cdot 1.5b^2c^5$

Simplify:
$(-2.8 \cdot 1.5)b^{3+2}c^{7+5} = -4.2b^5c^{12}$

3. Возведите в степень:

a) $(2x^3y)^3$

Apply power rule:
$(2^3)(x^{3 \cdot 3})(y^3) = 8x^9y^3$

b) $(-5a^4b^2c^3)^2$

Simplify:
$((-5)^2)(a^{4 \cdot 2})(b^{2 \cdot 2})(c^{3 \cdot 2}) = 25a^8b^4c^6$

4. Приведение подобных слагаемых:

a) $4a^2b - 3ab^2 + a^2b + 2ab^2$

Group similar terms:
$(4a^2b + a^2b) + (-3ab^2 + 2ab^2) = 5a^2b - ab^2$

b) $x^2 + 4x - 5 + x^2 - 3x + 2$

Group similar terms:
$(x^2 + x^2) + (4x - 3x) + (-5 + 2) = 2x^2 + x - 3$

5. Упростите выражение:

a) $(6x^2 - 7x + 4) - (4x^2 - 7x + 18)$

Simplify:
$6x^2 - 7x + 4 - 4x^2 + 7x - 18 = 2x^2 - 14$

b) $(3x + 9) + (-x^2 - 15x - 40)$

Simplify:
$3x + 9 - x^2 - 15x - 40 = -x^2 - 12x - 31$

c) $(10a^3 - 6a + 5) - (-11a + a^3 + 6)$

Simplify:
$10a^3 - 6a + 5 + 11a - a^3 - 6 = 9a^3 + 5a - 1$

Would you like me to elaborate on any of these solutions?

Follow-up Questions:

1. Can you explain the general rule for combining like terms?
2. What is the best way to simplify products of monomials?
3. How can we identify coefficients quickly in complex expressions?
4. Can you show more examples of raising monomials to powers?
5. What are the steps to subtract polynomials systematically?

Tip:

When raising a monomial to a power, apply the exponent to both coefficients and each variable individually.