Using the product rule: 5⁻² × 5⁻⁶ = 5⁻⁸ = 1/5⁸ = 1/390625

Apply exponent rules for multiplication and division.

Using the product rule: aᵐ × aⁿ = aᵐ⁺ⁿ 2⁻³ × 2⁻⁴ = 2⁻⁷ = 1/2⁷ = 1/128

Using the power of a product rule: (a × b)³ = a³ × b³ (3 × 2)³ = 3³ × 2³ = 27 × 8 = 216

Using the power of a product rule: (a × b)ⁿ = aⁿ × bⁿ (2 × 3)⁴ = 2⁴ × 3⁴ = 16 × 81 = 1296

Using the product rule: 8² × 8³ = 8⁵ Now, 8⁵ ÷ 8⁴ = 8⁵⁻⁴ = 8¹ = 8

Apply exponent rules for multiplication and division.

Using the power of a quotient rule: (a/b)ⁿ = aⁿ/bⁿ (2/3)³ = 2³/3³ = 8/27

Using the product rule: 7² × 7⁵ = 7⁷ Now, 7⁷ ÷ 7⁴ = 7⁷⁻⁴ = 7³ = 343

Using the product rule: 9² × 9⁴ = 9⁶ Now, 9⁶ ÷ 9³ = 9⁶⁻³ = 9³ = 729

Using the product rule: aᵐ × aⁿ = aᵐ⁺ⁿ 5³ × 5⁻² = 5³⁻² = 5¹ = 5

Using the rule: a^(m/n) = (n√a)ᵐ (32)^(3/5) = (⁵√32)³ = 2³ = 8

Using the product rule: aᵐ × aⁿ = aᵐ⁺ⁿ 3⁻⁵ × 3² = 3⁻⁵⁺² = 3⁻³ = 1/3³ = 1/27

2⁵ = 32.

Using the product rule: 7⁻² × 7⁻³ = 7⁻⁵ = 1/7⁵ = 1/16807

Apply exponent rules for multiplication and division.

Using the rule: a^(m/n) = (n√a)ᵐ (27)^(2/3) = (³√27)² = 3² = 9

Using the product rule: 5³ × 5² = 5⁵ Now, 5⁵ ÷ 5⁴ = 5⁵⁻⁴ = 5¹ = 5

Using the product rule: 2⁴ × 2⁻² = 2⁴⁻² = 2² Now, 2² × 2³ = 2²⁺³ = 2⁵ = 32

Using the product rule: 2⁻² × 2⁻⁴ = 2⁻⁶ = 1/2⁶ = 1/64