Rational exponents and the laws of exponents

Grade 9 Math Worksheet

Circle the best answer.

1. 1.

   Kira writes (x^6)^(1/2) as one power of x, for x > 0. Which is it?

   • x^12
   • x^(13/2)
   • x³
   • x^(1/6)
2. 2.

   Ari writes (x^12)^(1/3) as one power of x, for x > 0. Which is it?

   • x⁴
   • x^(37/3)
   • x^(1/12)
   • x^36
3. 3.

   Tala writes (27x^9)^(1/3) in simplest form, for x > 0. Which is it?

   • 9x³
   • 3x^27
   • 3x³
   • 27x³
4. 4.

   Bacteria multiply by 16 every day at a steady rate. Noah wants the factor for one quarter of a day. By what factor do they multiply?

   • 4
   • 2
   • 4.75
   • 65,536
5. 5.

   Ren enlarges a square quilt so its area is 9 times the old area. Each side is multiplied by what factor?

   • 3
   • 9
   • about 2.1
   • 4.5
6. 6.

   A cube-shaped box's volume becomes 64 times as big. Bo wants the factor for each edge. By what factor is each edge multiplied?

   • 64
   • 8
   • about 21.3
   • 4
7. 7.

   Tala's cube-shaped planter has edge 30 cm. A bigger similar cube holds 8 times as much soil. What is the new edge?

   • about 84.9 cm
   • 80 cm
   • 240 cm
   • 60 cm
8. 8.

   A rectangular poster is reduced to 1/4 of its area, keeping its shape. Its width was 40 cm. Milo finds the new width. What is it?

   • 20 cm
   • 5 cm
   • about 25.2 cm
   • 10 cm
9. 9.

   Pia's robot screen shows 25^(-1/2), a power with a minus sign. What is its value?

   • 1/5
   • -5
   • 5
   • 2/25
10. 10.

    Ari's lock code is 64^(-1/3), a power with a minus sign. What is its value?

    • 3/64
    • 4
    • 1/4
    • -4