Rational exponents and the laws of exponents
Grade 9 Math Worksheet - Challenge Me
Circle the best answer.
A town's population multiplies by 81 over 4 years at a steady yearly factor f. Kira wants f. What is it?
- 20.25
- 3
- 21
- 9
A video's views multiply by 8 over 3 weeks at a steady weekly factor f. Luz wants f. What is it?
- 2
- about 2.67
- about 2.83
- about 3.33
An account multiplies by 25 in one year at a steady rate. Jun wants the factor for each half-year. What is it?
- about 2.9
- 12.5
- 13
- 5
Noah writes 9^(1/2) + 16^(1/2) = 25^(1/2) = 5. Which response is correct?
- Yes: powers with the same exponent add their bases, so the sum is 25^(1/2) = 5.
- No: a half power halves the base, so 9^(1/2) + 16^(1/2) = 4.5 + 8 = 12.5.
- No: 9^(1/2) + 16^(1/2) = 3 + 4 = 7, but 25^(1/2) = 5, so the sum cannot be combined.
- No: the exponents add too, so 9^(1/2) + 16^(1/2) = 25^1 = 25.
Pia writes 4^(1/2) × 9^(1/2) = 36^(1/2) = 6, then checks by finding each root first. Is the step right?
- No: the bases 4 and 9 differ, so the product cannot be rewritten as one power.
- No: multiplying powers adds exponents, so 4^(1/2) × 9^(1/2) = 36^1 = 36.
- Yes: 4^(1/2) × 9^(1/2) = 2 × 3 = 6, and 36^(1/2) = 6, so the two roots multiply.
- No: a half power halves the base, so 4^(1/2) × 9^(1/2) = 2 × 4.5 = 9.
Tala writes (2^(1/3))^6 = 2^(1/18), because the exponents multiply. Which response is correct?
- No: six copies add, so (2^(1/3))^6 = 6 × 2^(1/3), about 7.6.
- No: 1/3 × 6 = 2, so (2^(1/3))^6 = 2² = 4.
- No: the exponents add, so (2^(1/3))^6 = 2^(19/3).
- Yes: the 6 goes under the 3, so the exponent is 1/18 and the value is 2^(1/18).
Ren solves (x - 2)^(1/2) = 6 for x. What is x?
- 36
- 34
- 38
- about 4.4
Bo solves (x + 5)^(1/3) = 2 for x. What is x?
- 13
- 8
- 3
- -1
Esme solves (x + 3)^(1/2) = 5 for x. What is x?
- 22
- 28
- 7
- 25
Zee solves 2 × x^(1/3) = 8 for x. What is x?
- 512
- 16
- 4
- 64