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Let's solve the exercise where we need to express each calculation as a single power.

### General Rule:
1. **Multiplication of powers with the same base**: \( a^m \cdot a^n = a^{m+n} \)
2. **Division of powers with the same base**: \( \frac{a^m}{a^n} = a^{m-n} \)
3. **Power of a power**: \( (a^m)^n = a^{m \cdot n} \)

### Solutions:
Let's go step by step for each part:

**a) \( g^5 \cdot g^2 \)**  
Using the multiplication rule, we add the exponents:  
\[ g^5 \cdot g^2 = g^{5+2} = g^7 \]

**b) \( 7^8 \div 7^4 \)**  
Using the division rule, we subtract the exponents:  
\[ \frac{7^8}{7^4} = 7^{8-4} = 7^4 \]

**c) \( 4^5 \cdot 4^3 \div 4^2 \)**  
First, multiply the powers, then divide:  
\[ (4^5 \cdot 4^3) \div 4^2 = 4^{5+3-2} = 4^6 \]

**d) \( 6^2 \cdot 6^3 \)**  
Using the multiplication rule:  
\[ 6^2 \cdot 6^3 = 6^{2+3} = 6^5 \]

**e) \( 2^5 \cdot 2^3 \cdot 2^0 \)**  
Using the multiplication rule (remember that \( 2^0 = 1 \)):  
\[ 2^5 \cdot 2^3 \cdot 2^0 = 2^{5+3+0} = 2^8 \]

**f) \( 3^4 \cdot 3 \)**  
Remember that \( 3 = 3^1 \), so:  
\[ 3^4 \cdot 3 = 3^{4+1} = 3^5 \]

**g) \( (8^2)^3 \)**  
Using the power of a power rule:  
\[ (8^2)^3 = 8^{2 \cdot 3} = 8^6 \]

**h) \( (5^5)^6 \)**  
Again, using the power of a power rule:  
\[ (5^5)^6 = 5^{5 \cdot 6} = 5^{30} \]

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If you have any questions or need further explanation, feel free to ask!

Here are 5 related questions you might find helpful:
1. What happens if the bases are different when multiplying powers?
2. How do you simplify a product of powers with different bases but the same exponent?
3. Can you explain the result when raising a base to the power of zero?
4. How do you simplify a fraction with powers that have different bases?
5. What happens when a power is negative?

**Tip:** Always double-check that the base is the same before applying exponent rules like multiplication or division of powers.

Expresar cada cálculo en una sola potencia.

Learn how to simplify exponent calculations using multiplication and division rules, as well as the power of a power rule. This exercise helps students understand how to express each calculation as a single power, perfect for Grades 7-9.

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