1) 4² + 3² · 3³ =
2) 5⁶ · 5³ - 2² · 2³ =
3) (8 - 7)³ + 14⁶ : 14⁵ + 20⁰ =
4) 6³ - 7² - (10²)⁷ : 10¹² =
5) 2 · 3⁴ - 2² · 2² + 15 =

Q: 1) 4² + 3² · 3³ = 2) 5⁶ · 5³ - 2² · 2³ = 3) (8 - 7)³ + 14⁶ : 14⁵ + 20⁰ = 4) 6³ - 7² - (10²)⁷ : 10¹² = 5) 2 · 3⁴ - 2² · 2² + 15 =

Let's solve each expression: 1) $4^2 + 3^2 \cdot 3^3$ \[ 4^2 = 16 \] \[ 3^2 = 9 \] \[ 3^3 = 27 \] \[ 3^2 \cdot 3^3 = 9 \cdot 27 = 243 \] \[ 4^2 + 3^2 \cdot 3^3 = 16 + 243 = 259 \] 2) $5^6 \cdot 5^3 - 2^2 \cdot 2^3$ \[ 5^6 = 15625 \] \[ 5^3 = 125 \] \[ 5^6 \cdot 5^3 = 15625 \cdot 125 = 1953125 \] \[ 2^2 = 4 \] \[ 2^3 = 8 \] \[ 2^2 \cdot 2^3 = 4 \cdot 8 = 32 \] \[ 5^6 \cdot 5^3 - 2^2 \cdot 2^3 = 1953125 - 32 = 1953093 \] 3) $(8 - 7)^3 + 14^6 \cdot 14^5 + 20^0$ \[ 8 - 7 = 1 \] \[ 1^3 = 1 \] \[ 14^6 \cdot 14^5 = 14^{11} \] \[ 20^0 = 1 \] \[ (8 - 7)^3 + 14^6 \cdot 14^5 + 20^0 = 1 + 14^{11} + 1 \] Note: $14^{11}$ is a large number and can be calculated if needed. 4) $6^3 \cdot 7^2 - (10^2)^7 \cdot 10^{12}$ \[ 6^3 = 216 \] \[ 7^2 = 49 \] \[ 6^3 \cdot 7^2 = 216 \cdot 49 = 10584 \] \[ 10^2 = 100 \] \[ (10^2)^7 = 100^7 = 10^{14} \] \[ 10^{14} \cdot 10^{12} = 10^{26} \] \[ 6^3 \cdot 7^2 - (10^2)^7 \cdot 10^{12} = 10584 - 10^{26} \] Note: $10^{26}$ is a very large number, making this expression negative. 5) $2 \cdot 3^4 - 2^2 \cdot 2^2 + 15$ \[ 3^4 = 81 \] \[ 2 \cdot 3^4 = 2 \cdot 81 = 162 \] \[ 2^2 = 4 \] \[ 2^2 \cdot 2^2 = 4 \cdot 4 = 16 \] \[ 162 - 16 + 15 = 161 \] If you need further calculations or clarifications, let me know!

Question

Accepted Answer

Let's solve each expression:

1) $4^2 + 3^2 \cdot 3^3$

$$
4^2 = 16
$$
$$
3^2 = 9
$$
$$
3^3 = 27
$$
$$
3^2 \cdot 3^3 = 9 \cdot 27 = 243
$$
$$
4^2 + 3^2 \cdot 3^3 = 16 + 243 = 259
$$

2) $5^6 \cdot 5^3 - 2^2 \cdot 2^3$

$$
5^6 = 15625
$$
$$
5^3 = 125
$$
$$
5^6 \cdot 5^3 = 15625 \cdot 125 = 1953125
$$
$$
2^2 = 4
$$
$$
2^3 = 8
$$
$$
2^2 \cdot 2^3 = 4 \cdot 8 = 32
$$
$$
5^6 \cdot 5^3 - 2^2 \cdot 2^3 = 1953125 - 32 = 1953093
$$

3) $(8 - 7)^3 + 14^6 \cdot 14^5 + 20^0$

$$
8 - 7 = 1
$$
$$
1^3 = 1
$$
$$
14^6 \cdot 14^5 = 14^{11}
$$
$$
20^0 = 1
$$
$$
(8 - 7)^3 + 14^6 \cdot 14^5 + 20^0 = 1 + 14^{11} + 1
$$

Note: $14^{11}$ is a large number and can be calculated if needed.

4) $6^3 \cdot 7^2 - (10^2)^7 \cdot 10^{12}$

$$
6^3 = 216
$$
$$
7^2 = 49
$$
$$
6^3 \cdot 7^2 = 216 \cdot 49 = 10584
$$
$$
10^2 = 100
$$
$$
(10^2)^7 = 100^7 = 10^{14}
$$
$$
10^{14} \cdot 10^{12} = 10^{26}
$$
$$
6^3 \cdot 7^2 - (10^2)^7 \cdot 10^{12} = 10584 - 10^{26}
$$

Note: $10^{26}$ is a very large number, making this expression negative.

5) $2 \cdot 3^4 - 2^2 \cdot 2^2 + 15$

$$
3^4 = 81
$$
$$
2 \cdot 3^4 = 2 \cdot 81 = 162
$$
$$
2^2 = 4
$$
$$
2^2 \cdot 2^2 = 4 \cdot 4 = 16
$$
$$
162 - 16 + 15 = 161
$$

If you need further calculations or clarifications, let me know!