Find m so that $(-3)^{m+1} imes(-3)^5 = (-3)^7$

Q: Find m so that $(-3)^{m+1}\times(-3)^5 = (-3)^7$

To solve the problem, we need to find the value of $ m $ such that the equation $(-3)^{m+1} \times (-3)^5 = (-3)^7$ holds true. ### Explanation: 1. **Understanding the Equation:** - The equation given is $(-3)^{m+1} \times (-3)^5 = (-3)^7$. - According to the laws of exponents, when multiplying powers with the same base, we add the exponents. Therefore, the left side of the equation can be simplified as: \[ (-3)^{m+1} \times (-3)^5 = (-3)^{(m+1) + 5} \] - This simplifies to: \[ (-3)^{m+1+5} = (-3)^{m+6} \] 2. **Setting the Exponents Equal:** - For the equation $(-3)^{m+6} = (-3)^7$ to be true, the exponents must be equal because the bases are the same. Therefore, we set: \[ m + 6 = 7 \] 3. **Solving for $ m $:** - Subtract 6 from both sides to solve for $ m $: \[ m = 7 - 6 \] - Thus, $ m = 1 $. ### Justification for Option 3: - **Option 3 is Correct:** - The calculation shows that $ m = 1 $, which corresponds to Option 3. Therefore, Option 3 is the correct answer. ### Explanation for Incorrect Options: - **Option 1 (m = 4):** - If $ m = 4 $, then $ m + 6 = 10 $, which does not equal 7. Therefore, this option is incorrect. - **Option 2 (m = 2):** - If $ m = 2 $, then $ m + 6 = 8 $, which does not equal 7. Therefore, this option is incorrect. - **Option 4 (m = 0):** - If $ m = 0 $, then $ m + 6 = 6 $, which does not equal 7. Therefore, this option is incorrect. In conclusion, the correct value of $ m $ that satisfies the equation is 1, making Option 3 the correct choice.

Question

Find m so that $(-3)^{m+1}	imes(-3)^5 = (-3)^7$

Accepted Answer

To solve the problem, we need to find the value of $ m $ such that the equation $(-3)^{m+1} \times (-3)^5 = (-3)^7$ holds true.

### Explanation:

1. **Understanding the Equation:**
   - The equation given is $(-3)^{m+1} \times (-3)^5 = (-3)^7$.
   - According to the laws of exponents, when multiplying powers with the same base, we add the exponents. Therefore, the left side of the equation can be simplified as:
     $$
     (-3)^{m+1} \times (-3)^5 = (-3)^{(m+1) + 5}
     $$
   - This simplifies to:
     $$
     (-3)^{m+1+5} = (-3)^{m+6}
     $$

2. **Setting the Exponents Equal:**
   - For the equation $(-3)^{m+6} = (-3)^7$ to be true, the exponents must be equal because the bases are the same. Therefore, we set:
     $$
     m + 6 = 7
     $$

3. **Solving for $ m $:**
   - Subtract 6 from both sides to solve for $ m $:
     $$
     m = 7 - 6
     $$
   - Thus, $ m = 1 $.

### Justification for Option 3:

- **Option 3 is Correct:**
  - The calculation shows that $ m = 1 $, which corresponds to Option 3. Therefore, Option 3 is the correct answer.

### Explanation for Incorrect Options:

- **Option 1 (m = 4):**
  - If $ m = 4 $, then $ m + 6 = 10 $, which does not equal 7. Therefore, this option is incorrect.

- **Option 2 (m = 2):**
  - If $ m = 2 $, then $ m + 6 = 8 $, which does not equal 7. Therefore, this option is incorrect.

- **Option 4 (m = 0):**
  - If $ m = 0 $, then $ m + 6 = 6 $, which does not equal 7. Therefore, this option is incorrect.

In conclusion, the correct value of $ m $ that satisfies the equation is 1, making Option 3 the correct choice.