Exponents and Roots — Practice Problems and Worked Solutions

The formulas you need here

16 worked problems

Every step is generated and checked by a computer algebra system.

1. 1.

   Evaluate the powers and roots.

   $$2^3$$

   Answer: $8$

   Step-by-step solution

   1. $$\text{Read an exponent as repeated multiplication.}$$
   2. $$\text{A square root asks which nonnegative number squares to the radicand.}$$
   3. $$=8$$
2. 2.

   Evaluate the powers and roots.

   $$(-3{)}^2$$

   Answer: $9$

   Step-by-step solution

   1. $$\text{Read an exponent as repeated multiplication.}$$
   2. $$\text{A square root asks which nonnegative number squares to the radicand.}$$
   3. $$=9$$
3. 3.

   Evaluate the powers and roots.

   $$\sqrt{49}$$

   Answer: $7$

   Step-by-step solution

   1. $$\text{Read an exponent as repeated multiplication.}$$
   2. $$\text{A square root asks which nonnegative number squares to the radicand.}$$
   3. $$=7$$
4. 4.

   Evaluate the powers and roots.

   $$2^3\cdot 2^2$$

   Answer: $32$

   Step-by-step solution

   1. $$\text{Read an exponent as repeated multiplication.}$$
   2. $$\text{A square root asks which nonnegative number squares to the radicand.}$$
   3. $$=32$$
5. 5.

   Evaluate the powers and roots.

   $$(3^2{)}^2$$

   Answer: $81$

   Step-by-step solution

   1. $$\text{Read an exponent as repeated multiplication.}$$
   2. $$\text{A square root asks which nonnegative number squares to the radicand.}$$
   3. $$=81$$
6. 6.

   Evaluate the powers and roots.

   $$\sqrt{144}+2^3$$

   Answer: $20$

   Step-by-step solution

   1. $$\text{Read an exponent as repeated multiplication.}$$
   2. $$\text{A square root asks which nonnegative number squares to the radicand.}$$
   3. $$=20$$
7. 7.

   Evaluate the powers and roots.

   $$3^3$$

   Answer: $27$

   Step-by-step solution

   1. $$\text{Read an exponent as repeated multiplication.}$$
   2. $$\text{A square root asks which nonnegative number squares to the radicand.}$$
   3. $$=27$$
8. 8.

   Evaluate the powers and roots.

   $$(-2{)}^4$$

   Answer: $16$

   Step-by-step solution

   1. $$\text{Read an exponent as repeated multiplication.}$$
   2. $$\text{A square root asks which nonnegative number squares to the radicand.}$$
   3. $$=16$$
9. 9.

   Evaluate the powers and roots.

   $$\sqrt{81}$$

   Answer: $9$

   Step-by-step solution

   1. $$\text{Read an exponent as repeated multiplication.}$$
   2. $$\text{A square root asks which nonnegative number squares to the radicand.}$$
   3. $$=9$$
10. 10.

    Evaluate the powers and roots.

    $$3^2\cdot 3^3$$

    Answer: $243$

    Step-by-step solution

    1. $$\text{Read an exponent as repeated multiplication.}$$
    2. $$\text{A square root asks which nonnegative number squares to the radicand.}$$
    3. $$=243$$
11. 11.

    Evaluate the powers and roots.

    $$(2^3{)}^2$$

    Answer: $64$

    Step-by-step solution

    1. $$\text{Read an exponent as repeated multiplication.}$$
    2. $$\text{A square root asks which nonnegative number squares to the radicand.}$$
    3. $$=64$$
12. 12.

    Evaluate the powers and roots.

    $$\sqrt{100}+3^2$$

    Answer: $19$

    Step-by-step solution

    1. $$\text{Read an exponent as repeated multiplication.}$$
    2. $$\text{A square root asks which nonnegative number squares to the radicand.}$$
    3. $$=19$$
13. 13.

    Evaluate the powers and roots.

    $$5^2$$

    Answer: $25$

    Step-by-step solution

    1. $$\text{Read an exponent as repeated multiplication.}$$
    2. $$\text{A square root asks which nonnegative number squares to the radicand.}$$
    3. $$=25$$
14. 14.

    Evaluate the powers and roots.

    $$\sqrt{64}$$

    Answer: $8$

    Step-by-step solution

    1. $$\text{Read an exponent as repeated multiplication.}$$
    2. $$\text{A square root asks which nonnegative number squares to the radicand.}$$
    3. $$=8$$
15. 15.

    Evaluate the powers and roots.

    $$2^5$$

    Answer: $32$

    Step-by-step solution

    1. $$\text{Read an exponent as repeated multiplication.}$$
    2. $$\text{A square root asks which nonnegative number squares to the radicand.}$$
    3. $$=32$$
16. 16.

    Evaluate the powers and roots.

    $$\sqrt{25}\cdot 2^2$$

    Answer: $20$

    Step-by-step solution

    1. $$\text{Read an exponent as repeated multiplication.}$$
    2. $$\text{A square root asks which nonnegative number squares to the radicand.}$$
    3. $$=20$$

More from Math Foundations

• Order of Operations
• Signed Numbers
• Fraction Sense
• Ratios and Percentages
• Algebraic Expressions
• Linear Equations
• Polynomial Basics
• Inequalities
• Coordinate Plane
• Reading Graphs
• Function Machines
• Substitution
• Factoring Basics