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.