Certainly! Let's dive into some practice problems involving indices (also known as exponents) and roots (such as square roots, cube roots, etc.). I'll provide a mix of problems, including simplifying expressions and solving equations.

### Indices Practice

1. **Simplify:**  
   \[
   (2^3) \times (2^4)
   \]
   
2. **Simplify:**  
   \[
   \frac{5^6}{5^2}
   \]

3. **Simplify:**  
   \[
   (3^2)^3
   \]

4. **Solve for \(x\):**  
   \[
   2^x = 16
   \]

5. **Simplify:**  
   \[
   (7^0) + (4^{-1})
   \]

### Roots Practice

1. **Simplify:**  
   \[
   \sqrt{49}
   \]

2. **Simplify:**  
   \[
   \sqrt[3]{27}
   \]

3. **Simplify:**  
   \[
   \sqrt{81} \times \sqrt{4}
   \]

4. **Solve for \(x\):**  
   \[
   x^2 = 25
   \]

5. **Simplify:**  
   \[
   \sqrt{\frac{1}{16}}
   \]

### Answers:

**Indices:**

1. \( (2^3) \times (2^4) = 2^{3+4} = 2^7 = 128 \)
2. \( \frac{5^6}{5^2} = 5^{6-2} = 5^4 = 625 \)
3. \( (3^2)^3 = 3^{2 \times 3} = 3^6 = 729 \)
4. \( 2^x = 16 \)  
   Since \( 2^4 = 16 \), \( x = 4 \)
5. \( (7^0) + (4^{-1}) = 1 + \frac{1}{4} = 1.25 \)

**Roots:**

1. \( \sqrt{49} = 7 \)
2. \( \sqrt[3]{27} = 3 \)
3. \( \sqrt{81} \times \sqrt{4} = 9 \times 2 = 18 \)
4. \( x^2 = 25 \)  
   \( x = \pm5 \)
5. \( \sqrt{\frac{1}{16}} = \frac{1}{4} \)

Would you like any details on the solutions? Feel free to ask if you have any questions!

### Additional Practice Questions:

1. Simplify: \(\frac{8^5}{8^3}\)
2. Simplify: \(\sqrt[4]{16}\)
3. Solve for \(x\): \(3^x = 81\)
4. Simplify: \((2^3)^2\)
5. Solve for \(x\): \(x^3 = 64\)

### Tip:
When multiplying or dividing powers with the same base, remember to add or subtract the exponents, respectively.

Explore practice problems involving indices (exponents) and roots (square roots, cube roots). Includes problems on simplifying expressions and solving equations. Perfect for high school students studying algebra and pre-calculus.

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