6.1 Extra Practice In Exercises 1-6, evaluate the expression. $$ \begin{array}{lll} ext { 1. } 5^{-4} & ext { 2. }(-5)^{-4} & ext { 3. } \frac{7^{-1}}{-8^{0}} \ ext { 4. } \frac{8^{-2}}{(-4)^{0}} & ext { 5. } \frac{-2^{-4}}{3^{-3}} & ext { 6. } \frac{6^{-2}}{(-1)^{-4}}\end{array} $$ In Exercises $$ 7-21 $$, simplify the expression. Write your answer using only $$ p $$

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6.1 Extra Practice In Exercises 1-6, evaluate the expression. $$ \begin{array}{lll}	ext { 1. } 5^{-4} & 	ext { 2. }(-5)^{-4} & 	ext { 3. } \frac{7^{-1}}{-8^{0}} \ 	ext { 4. } \frac{8^{-2}}{(-4)^{0}} & 	ext { 5. } \frac{-2^{-4}}{3^{-3}} & 	ext { 6. } \frac{6^{-2}}{(-1)^{-4}}\end{array} $$ In Exercises $$ 7-21 $$, simplify the expression. Write your answer using only $$ p $$

UpStudy AI · Accepted Answer

Sure! Let's evaluate and simplify each of the given expressions step by step.

### **Exercises 1-6: Evaluate the Expression**

1. **$$5^{-4}$$**
   $$
   5^{-4} = \frac{1}{5^4} = \frac{1}{625}
   $$

2. **$$(-5)^{-4}$$**
   $$
   (-5)^{-4} = \frac{1}{(-5)^4} = \frac{1}{625}
   $$
   *Since the exponent is even, the negative base becomes positive.*

3. **$$\frac{7^{-1}}{-8^{0}}$$**
   $$
   7^{-1} = \frac{1}{7^1} = \frac{1}{7}
   $$
   $$
   -8^{0} = -1 \quad (\text{Any non-zero number to the power of 0 is } 1)
   $$
   $$
   \frac{7^{-1}}{-8^{0}} = \frac{\frac{1}{7}}{-1} = -\frac{1}{7}
   $$

4. **$$\frac{8^{-2}}{(-4)^{0}}$$**
   $$
   8^{-2} = \frac{1}{8^2} = \frac{1}{64}
   $$
   $$
   (-4)^{0} = 1 \quad (\text{Any non-zero number to the power of 0 is } 1)
   $$
   $$
   \frac{8^{-2}}{(-4)^{0}} = \frac{\frac{1}{64}}{1} = \frac{1}{64}
   $$

5. **$$\frac{-2^{-4}}{3^{-3}}$$**
   $$
   -2^{-4} = -\left(\frac{1}{2^4}\right) = -\frac{1}{16}
   $$
   $$
   3^{-3} = \frac{1}{3^3} = \frac{1}{27}
   $$
   $$
   \frac{-2^{-4}}{3^{-3}} = \frac{-\frac{1}{16}}{\frac{1}{27}} = -\frac{1}{16} \times \frac{27}{1} = -\frac{27}{16}
   $$

6. **$$\frac{6^{-2}}{(-1)^{-4}}$$**
   $$
   6^{-2} = \frac{1}{6^2} = \frac{1}{36}
   $$
   $$
   (-1)^{-4} = \frac{1}{(-1)^4} = \frac{1}{1} = 1 \quad (\text{Since } (-1)^4 = 1)
   $$
   $$
   \frac{6^{-2}}{(-1)^{-4}} = \frac{\frac{1}{36}}{1} = \frac{1}{36}
   $$

### **Summary of Answers**

1. $$5^{-4} = \dfrac{1}{625}$$

2. $$(-5)^{-4} = \dfrac{1}{625}$$

3. $$\dfrac{7^{-1}}{-8^{0}} = -\dfrac{1}{7}$$

4. $$\dfrac{8^{-2}}{(-4)^{0}} = \dfrac{1}{64}$$

5. $$\dfrac{-2^{-4}}{3^{-3}} = -\dfrac{27}{16}$$

6. $$\dfrac{6^{-2}}{(-1)^{-4}} = \dfrac{1}{36}$$

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**Note on Exercises 7-21:**

You mentioned simplifying expressions using only $$ p $$ for Exercises 7-21, but the specific expressions to simplify haven't been provided. If you share the particular problems or expressions, I'd be happy to help you simplify them!
Here are the simplified answers for Exercises 1-6: 1. $$5^{-4} = \dfrac{1}{625}$$ 2. $$(-5)^{-4} = \dfrac{1}{625}$$ 3. $$\dfrac{7^{-1}}{-8^{0}} = -\dfrac{1}{7}$$ 4. $$\dfrac{8^{-2}}{(-4)^{0}} = \dfrac{1}{64}$$ 5. $$\dfrac{-2^{-4}}{3^{-3}} = -\dfrac{27}{16}$$ 6. $$\dfrac{6^{-2}}{(-1)^{-4}} = \dfrac{1}{36}$$ For Exercises 7-21, please provide the specific expressions to simplify using only $$ p $$.

6.1 Extra Practice
In Exercises 1-6, evaluate the expression.

In Exercises , simplify the expression. Write your answer using only

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6.1 Extra Practice In Exercises 1-6, evaluate the expression. In Exercises , simplify the expression. Write your answer using only