Sure! Let's solve the additional practice problems step by step.

1. Simplify: $\frac{8^5}{8^3}$

Solution: $\frac{8^5}{8^3} = 8^{5-3} = 8^2 = 64$

2. Simplify: $\sqrt[4]{16}$

Solution: $\sqrt[4]{16} = 2$ (Here, $2^4 = 16$, so the fourth root of 16 is 2.)

3. Solve for $x$: $3^x = 81$

Solution: $3^x = 81$ Since $81 = 3^4$, we have: $x = 4$

4. Simplify: $(2^3)^2$

Solution: $(2^3)^2 = 2^{3 \times 2} = 2^6 = 64$

5. Solve for $x$: $x^3 = 64$

Solution: $x^3 = 64$ Taking the cube root of both sides: $x = \sqrt[3]{64} = 4$ (Here, $4^3 = 64$.)

Would you like more problems or details on these solutions?

Related Practice Questions:

1. Simplify: $\frac{9^4}{9^2}$
2. Simplify: $\sqrt[3]{125}$
3. Solve for $x$: $2^{2x} = 32$
4. Simplify: $(5^2)^3$
5. Solve for $x$: $x^4 = 81$

Tip:

When solving equations involving exponents, express both sides with the same base if possible, then equate the exponents to find the solution.