Let’s evaluate the given expressions.

1. $(-7)^2$

   • Squaring means multiplying the base $(-7)$ by itself: $(-7) \times (-7) = 49$ So, $(-7)^2 = 49$.

2. $(-4)^3$

   • Cubing means multiplying the base $(-4)$ by itself three times: $(-4) \times (-4) \times (-4)$ First, multiply the first two terms: $(-4) \times (-4) = 16$ Then multiply the result by $(-4)$: $16 \times (-4) = -64$ So, $(-4)^3 = -64$.

Final Results:

1. $(-7)^2 = 49$
2. $(-4)^3 = -64$

Let me know if you need further clarification or have additional questions!

Related Questions:

1. What happens when we raise a negative number to an even power?
2. How does raising a negative number to an odd power affect the sign of the result?
3. Can you apply these concepts to solve real-world problems involving powers?
4. How are these rules used in algebraic expressions involving variables?
5. How does the distributive property relate to powers and exponents?

Tip:

Remember, negative bases raised to even powers always result in positive values, while odd powers maintain the negative sign!