Reduce radical expressions

CONCEPTS

Radicals

• Used to indicate a root

• ⁿ√x reads, x radical n or the nth root of x. It can also be written x¹ᐟⁿ

Properties

• (a/b)ˣ = aˣ / bˣ

• a⁻ˣ = 1 / aˣ

Tips

• Group terms when there re exponent expressions – 1) negatives, 2) numbers, 3) exponents with common bases

PRACTICE PROBLEMS

Question 1 Reduce (√4)⁻³

-- Answer -- 1 / 8

(2)⁻³ = 2⁻³ = 1 / 2³ = 1 / 8

Question 2 What is (8 / 3)⁻²ᐟ³

-- Answer -- 9¹ᐟ³ / 4

1 / (8 / 3)²ᐟ³ = 1 / (64 / 9)¹ᐟ³ = 1/(4 / 9¹ᐟ³) = 9¹ᐟ³ / 4

Question 3 Reduce (⁴√(9x))²(x⁵ᐟ²)

-- Answer -- 3x³

((9x)¹ᐟ⁴)² x⁴ = (9x)¹ᐟ² x⁵ᐟ² = 3x³

ACT PRACTICE PROBLEMS

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