Cube Roots and Rational Exponents

The video tutorial explains how to solve the equation x^3 = -64 by taking the cube root of both sides and using prime factorization to identify perfect cubes. It verifies the solution x = -4 and demonstrates an alternative method using rational exponents. The tutorial emphasizes understanding the properties of exponents and cube roots.

What is the first step in solving the equation x^3 = -64?

• Take the cube root of both sides

• Add 64 to both sides

• Take the square root of both sides

• Multiply both sides by 3

What is the prime factorization of 64?

• 2 x 32

• 2^6

• 4 x 16

• 8 x 8

How can we express 64 as a perfect cube?

• 2^3

• 4^3

• 16^1.5

• 8^2

What is the cube root of -64?

• 8

• -8

• -4

• 4

How do we verify the solution x = -4 for the equation x^3 = -64?

• By checking if -4^3 equals -64

• By checking if -4^2 equals 16

• By checking if -4 - 64 equals -68

• By checking if -4 + 64 equals 60

What property of exponents is used to solve x^3 = -64 using rational exponents?

• Zero exponent property

• Product of powers property

• Quotient of powers property

• Power of a power property

What is the reciprocal power used to solve x^3 = -64 using rational exponents?

• 2/3

• 3/2

• 1/2

• 1/3

How can the rational exponent 1/3 be expressed as a radical?

• Fifth root

• Square root

• Fourth root

• Cube root

What is the solution to the equation x^3 = -64?

• x = 4

• x = -4

• x = 8

• x = -8

Which method can be used to solve x^3 = -64?

• Only using radicals

• Using logarithms

• Only using rational exponents

• Using either radicals or rational exponents