Exploring Rational Exponents in Pre-Algebra

What does an exponent of 1/n represent?

• The number raised to the power of n

• The nth root of the number

• The number multiplied by n

• The number divided by n

How can the cube root of 'a' squared be represented using exponents?

• 'a' to the power of 2/3

• 'a' squared then cubed

• 'a' to the power of 3/2

• 'a' cubed then squared

What result do we get by squaring 'a' first and then taking the cube root?

• 'a' to the power of 3/2

• 'a' squared then cubed

• 'a' cubed then squared

• 'a' to the power of 2/3

What is the result of raising a base to a fractional exponent?

• The root specified by the denominator, then raised to the power of the numerator

• The base divided by the fraction

• The base raised to the power of the numerator, then the root specified by the denominator

• The base multiplied by the fraction

What does a negative rational exponent indicate?

• Division by the base

• One over the base raised to the positive rational exponent

• The base raised to the power of zero

• Multiplication by the base

Can fractional exponents be negative?

• Yes, indicating one over the base with a positive exponent

• No, negative exponents are not rational

• Yes, but only if the base is negative

• No, exponents must always be positive

How can one over the square root of x be written using exponents?

• 1/x

• x squared

• x to the power of 1/2

• x to the power of -1/2

How can the expression 'a' over the square root of 'a' be simplified?

• 1/'a'

• 'a' squared

• 'a' to the power of 1/2

• The square root of 'a'

What is the simplified form of the square root of 'a' over the cube root of 'a'?

• 'a' to the power of 1/2

• The sixth root of 'a'

• 'a' to the power of 1/3

• 'a' to the power of 1/6

What does the cube root of 'a' squared over the sixth root of 'a' simplify to?

• 'a' to the power of 1/2

• The square root of 'a'

• 'a' to the power of 2/3

• 'a' to the power of 1/6