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Powers and Exponents Practice Questions

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Updated on Apr 22, 2013

To review these concepts, go to Powers and Exponents Study Guide.

Powers and Exponents Practice Questions

Practice

  1. Evaluate 64.
  2. Circle the expression that is NOT equivalent to 5 · 5 · 5 · 5.  

    5 · 4   (5 · 5)2   54   5 · 53   625

  3. Evaluate cd2 – 1 when c = –1 and d = –6.
  4. The expression 4–2 is equivalent to ____.
  5. How can you simplify the expression 22 · 23?
  6. Simplify: a2b · ab3
  7. Simplify:
  8. Simplify: (3xy3)2

Solutions

  1. 64 is equal to 6 · 6 · 6 · 6. When multiplied together, the result is 1,296.
  2. 5 · 4 should be circled. This is equal to 20. The others are equivalent to 625.
  3. Substitute the values for the variables in the expression: (–1)(–6)2 – 1

     

    Evaluate the exponent: (–1)(–6)2 – 1

    Remember that (–6)2 = (–6)(–6) = 36.

    Multiply the first term: (–1)(36) – 1

    This simplifies to (–36) – 1. Evaluate by changing subtraction to addition and the sign of the second term to its opposite. Signs are the same, so add and keep the sign:

    (–36) + (–1) = –37

  4. When you evaluate a negative exponent, take the reciprocal of the base and make the exponent positive. Therefore, 4–2 is equivalent to , which simplifies to
  5. When you multiply like bases, add the exponents. The expression 22 · 23 is equivalent to 22 + 3, which simplifies to 25.
  6. When you multiply like bases, add the exponents. The expression a2b · ab3 can also be written as a2b1 · a1b3. Grouping like bases results in a2a1 · b1b3. Adding the exponents gives a2 + 1b1 + 3, which is equal to a3b4, the simplified answer.
  7. When you divide like bases, subtract the exponents. The expression then becomes x6 – 3, which simplifies to x3.
  8. When you raise a quantity to a power, raise each base to that power by multiplying the exponents. The expression (3xy3)2 equals 32x2y6, which simplifies to 9x2y6. Another way to look at this problem is to remember that when a quantity is squared, it is multiplied by itself. The expression (3xy3)2 becomes (3xy3) · (3xy3). Multiply coefficients and add the exponents of like bases: 3 · 3x1+ 1y3 + 3 simplifies to 9x2y6.
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