To review these concepts, go to Exponents Study Guide.
Exponents Practice Questions
Problems
Practice 1
Solve:
 (b^{2})^{3}
 (n^{6})^{6}
 3(v^{7})^{4}
 4(r^{5})^{10}
 5(3w^{8})^{2}
Practice 2
 (pqr)^{9}
 (3j^{6}k^{2})^{3}
 –10(2s^{8}t^{5})^{5}
 (u^{7})^{–6}
 5(e^{–5})^{12}
 (6a^{–11})^{3}
 (2z^{–2})^{–2}
 (g^{3}h^{–4})^{–4}
 (4p^{3}q^{8})^{0}
 2(k^{13}m^{0}n–1)^{–1}
Solutions
Practice 1

b^{2} is raised to the third power. Multiply the exponents: (2)(3) = 6, and (b^{2})^{3} = b^{6}.

n^{6} is raised to the sixth power. Multiply the exponents: (6)(6) = 36, and (n^{6})^{6} = n^{36}.

3v^{7} is raised to the fourth power.
Raise 3 to the fourth power and raise v^{7} to the fourth power: 3^{4} = 81.
To find (v^{7})^{4}, multiply the exponents: (7)(4) = 28, v^{7})^{4} = v^{28}, and (3v^{7})^{4} = 81v^{28}.

r^{5} is raised to the tenth power and multiplied by 4.
Exponents come first in the order of operations, so begin by raising r^{5} to the tenth power.
Multiply the exponents: (5)(10) = 50, and (r^{5})^{10} = r^{50}.
Finally, multiply by 4: (4)(r^{50}) = 4r^{50}.

3w^{8} is raised to the second power and multiplied by 4. Work with the exponent before multiplying.
Raise 3 to the second power and raise w^{8} to the second power. 32 = 9.
To find (w^{8})^{2}, multiply the exponents: (8)(2) = 16, (w^{8})^{2} = w^{16}, and (3w^{8})^{2} = 9w^{16}.
Finally, multiply 9w^{16} by 5: (5)(9w^{16}) = 45w^{16}.
Practice 2
 pqr is raised to the ninth power. Each variable has an exponent of 1, and each exponent must be multiplied by 9. Because (1)(9) = 9, the exponent of each variable is 9.
(pqr)^{9} = p^{9}q^{9}r^{9}
 (3j^{6}k^{2}) is raised to the third power. Each variable must have its exponent multiplied by 3, and the coefficient 3 must also be raised to the third power.
3^{3} = 27
(6)(3) = 18, so (j^{6})^{3} = j^{18}
(2)(3) = 6, so (k^{2})^{3} = k^{6}
(3j^{6}k^{2})^{3} = 27j^{18}k^{6}
 (2s^{8}t^{5}) is raised to the fifth power, and then multiplied by –10. Each variable must have its exponent multiplied by 5, and the coefficient 2 must also be raised to the fifth power.
2^{5} = 32
(8)(5) = 40, so (s^{8})^{5} = s^{40}
(5)(5) = 25, so (t^{5})^{5} = t^{25}
(2s^{8}t^{5})^{5} = 32s^{40}t^{25}
Finally, multiply by –10:
(–10)(32s^{40}t^{25}) = –320s^{40}t^{25}
 (u7) is raised to the negative sixth power. Multiply 7 by –6:
(7)(–6) = –42, so (u^{7})^{–6} = u^{–42}

(e–5) is raised to the 12th power, and then multiplied by 5. Multiply –5 by 12:
(–5)(12) = –60, so (e^{–5})^{12} = e^{–60}
Multiply e–60 by its coefficient, 5:
(5)(e^{–60}) = 5e^{–60}

(6a^{–11}) is raised to the third power. The variable a must have its exponent multiplied by 3, and the coefficient 6 must also be raised to the third power.
6^{3} = 216
(–11)(3) = –33, so (a^{–11})^{3} = a^{–33}
(6a^{–11})^{3} = 216a^{–33}

(2z^{–2}) is raised to the negative second power. The variable z must have its exponent multiplied by –2, and the coefficient 2 must also be raised to the negative second power. To raise 2 to the negative second power, place the 2 with an exponent of positive 2 in the denominator of a fraction with a numerator of 1:
(–2)(–2) = 4, so (z^{–2})^{–2} = z^{4}

(g^{3}h^{–4}) is raised to the negative eighth power. The variables g and h must each have their exponent multiplied by –8.
(3)(–8) = –24, so (g^{3})^{–8} = g^{–24}
(–4)(–8) = 32, so (h^{–4})^{–8} = h^{32}
(g^{3}h^{–4})^{–8} = g^{–24}h^{32}

The entire term in parentheses is raised to the zero power. Any quantity raised to the zero power is equal to 1.

(k^{13}m^{0}n^{–1}) is raised to the negative 1 power, and then multiplied by 2. The variables k and n must each have their exponent multiplied by –1. The variable m is raised to the zero power, so it is equal to 1. Because k^{13} and n^{–1} are multiplied by m^{0}=1, the m term drops out of the expression.
(13)(–1) = –13, so (k^{13})^{–1} = k^{–13}
(–1)(–1) = 1, so (n^{–1})^{–1} = n^{1}, or n
The expression is now 2(k^{–13}n). Multiply by 2:
(2)(k^{–13}n) = 2k^{–13}n
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