Answer: 3⁶

Explanation: When multiplying powers with the same base, add the exponents: 3² × 3⁴ = 3²⁺⁴ = 3⁶

Answer: 2⁶ = 64

Explanation: When raising a power to a power, multiply the exponents: (2³)² = 2³ˣ² = 2⁶ = 64

Answer: 5⁴

Explanation: When dividing powers with the same base, subtract the exponents: 5⁷ ÷ 5³ = 5⁷⁻³ = 5⁴

Answer: x³y³

Explanation: When raising a product to a power, raise each factor to that power: (xy)³ = x³y³

Answer: 1

Explanation: Any non-zero number raised to the power of 0 equals 1

Answer: 3⁷

Step-by-step solution:

First, simplify (3²)³ = 3²ˣ³ = 3⁶

Then multiply: 3⁶ × 3¹ = 3⁶⁺¹ = 3⁷

Answer: 16x¹²

Step-by-step solution:

(2x³)⁴ = 2⁴ × (x³)⁴ = 16 × x¹² = 16x¹²

Answer: x⁹

Step-by-step solution:

Work from left to right: x⁸ ÷ x² = x⁸⁻² = x⁶

Then: x⁶ × x³ = x⁶⁺³ = x⁹

Answer: a²b⁴

Step-by-step solution:

First: (a²b³)² = a⁴b⁶

Second: (ab)² = a²b²

Finally: a⁴b⁶ ÷ a²b² = a⁴⁻²b⁶⁻² = a²b⁴

Answer: x = 5

Explanation: Since 32 = 2⁵, we have 2ˣ = 2⁵, so x = 5

Answer: 3²

Step-by-step solution:

First: (3⁻²)³ = 3⁻⁶

Then: 3⁻⁶ × 3⁸ = 3⁻⁶⁺⁸ = 3²

Answer: 64 = 2⁶ and 64 = 4³

Explanation:

As a power of 2: 64 = 2 × 2 × 2 × 2 × 2 × 2 = 2⁶

As a power of 4: 64 = 4 × 4 × 4 = 4³