Laws of Rational Exponents

Write in exponential form

∛x⁷ = (x⁷)^1/3

• x⁷∕ ³

• x3⁄7

• 3x⁷

• 7x³

Write in exponential form

√x⁵ =( x⁵)^1/2

• X¹∕ ⁵

• X ²⁄⁵

• X⁵⁄ ²

• X⁵

Write in exponential form

∜(3x)³ = (3x)^(3*1/4)

• 3x³⁄ ⁴

• (3x)³∕ ⁴

• (3x)⁴⁄ ³

• 3x⁴⁄ ³

Write as a radical expression

y²⁄ ³= (y²)^1/3

• 2y³

• √y³

• ∛y²

• 3y²

Write as a radical expression

y¹⁄ ³

The 1/3 power equals the cube root.

• ∛y

• y³

• √y

• 1∕ 3y

Simplify

x²⁄ ³⋅x¹⁄ ³

add the exponents

• 2x

• x²⁄₉

• x

• x²

Simplify:

x⁻ ¹⁄ ² ⋅ x⁻¹⁄ ⁴

add the exponents

• -x¹∕ ⁶

• x ³∕ ⁴

• 1∕ x³⁄⁴

• x¹∕ ⁸

Simplify

(x²⁄ ³)²⁄ ⁵

Multiply the exponents

• x⁴∕ ¹⁵

• x¹⁶∕ ¹⁵

• x⁶

• 6x

Simplify
(x⁻²)⁻¹∕²

• 1∕ x³∕²
• 1∕ x²
• 1∕ x
• x

Simplify

x⅞ ⁄ x

Division - subtract the exponents

• x

• 1∕ x¹∕ ⁸

• 1∕8x

• x⁴