Exponents and Roots Concepts

The video tutorial explains how to simplify expressions with fractional exponents. It begins by rewriting decimal exponents as fractions and applies exponent rules to multiply exponents. The tutorial demonstrates simplifying expressions using common factors and converting expressions into radical form. It concludes with simplifying cube roots using prime factorization, showing that 8 raised to the power of -2/3 raised to the power of 0.5 equals 2.

What is the equivalent of 0.5 in fractional form?

• 1/2

• 1/3

• 3/4

• 2/3

Which rule is used to multiply exponents when powers are raised to powers?

• a^(m*n) = a^(m+n)

• a^m / a^n = a^(m-n)

• a^(m*n) = a^(m*n)

• a^m * a^n = a^(m+n)

What is the simplified form of 2/2?

• 3

• 2

• 1

• 0

How do you express 8^(1/3) in radical form?

• Square root of 8

• Cube root of 8

• Fourth root of 8

• Fifth root of 8

What is the exponent rule for a^(m/n)?

• Both numerator and denominator are indices

• Denominator is the index, numerator is the exponent

• Numerator is the index, denominator is the exponent

• Both numerator and denominator are exponents

What is the prime factorization of 8?

• 2 * 2 * 2

• 2 * 2 * 3

• 2 * 3

• 3 * 3

What is the cube root of 8?

• 2

• 1

• 3

• 4

What is the result of simplifying 8 raised to the power of -2/3?

• 1/4

• 1/2

• 1/8

• 1/16

What is the final simplified result of the expression 8^(-23)^(0.5)?

• Positive 2

• Positive 1

• Negative 2

• Negative 1

What is the simplified form of 8^(1/3) when the exponent is 1?

• 4

• 1

• 2

• 8