Understanding Rational Exponents

What is the square root of 81 expressed as a rational exponent?

• 81^2

• 81^1/2

• 81^1/3

• 81^3

Which of the following is the fourth root of 256?

• 4

• 2

• 8

• 16

How can 8 to the one-third power be expressed in radical form?

• Square root of 8

• Cube root of 8

• Fourth root of 8

• Fifth root of 8

What is the result of 32 to the two-fifths power?

• 32

• 16

• 8

• 4

If 9 to the x equals 729, what is the value of x?

• 5

• 4

• 3

• 2

How can 16 to the 2x minus 1 be rewritten using a base of 2?

• 2^(3x-2)

• 2^(4x-1)

• 2^(8x-4)

• 2^(2x-1)

Which of the following is a key step in solving equations with rational exponents?

• Adding exponents

• Finding a common base

• Multiplying bases

• Subtracting exponents

In the equation p = 40 * 2^(t/8), what does the variable t represent?

• Population size

• Time in hours

• Doubling rate

• Initial bacteria count

What is the value of t if p equals 20,480 in the equation p = 40 * 2^(t/8)?

• 80 hours

• 88 hours

• 72 hours

• 64 hours

What is the primary goal when working with rational exponents in equations?

• To decrease the exponent

• To increase the exponent

• To find the same base

• To simplify the base