Answer:

For power of a power, multiply the exponents.

For product of powers, add the exponents.

1. (8⅓) (8⅓) = 8⅔

Add ⅓ and ⅓.

⅓ + ⅓ = ⅔

Note: Write ⅔ as exponent.

2. (x⅔)¼ = x⅙

Multiply ⅔ by ¼

(⅔)(¼) = ²⁄₁₂ = ⅙

Note: Write ⅙ as exponent.

3. (3x½y) (4x⅔y½) = 12x⁷⁄₆y³⁄₂

for x: ½ + ⅔ = ³⁄₆ + ⁴⁄₆ = ⁷⁄₆

for y: 1 + ½ = ³⁄₂

Note: Write ⁷⁄₆ and ³⁄₂ as exponents of x and y, respectively.

4. (x⅘y⅗)½ = x⅖y³⁄₁₀

for x: (⅘)(½) = ⁴⁄₁₀ = ⅖

for y: (⅗)(½) = ³⁄₁₀

Note: Write ⅖ and ³⁄₁₀ as exponents of x and y, respectively

5. 120a⁴ 12a¹⁰⁄₃

-------------- = ----------

10a⅔b½ b½

120/10 = 12

for division, subtract the powers:

4 - ⅔ = ¹²⁄₃ - ⅔ = ¹⁰⁄₃

Note: Write ¹⁰⁄₃ and ½ as exponents.