Exponent Rules
See how to use the exponent rules
to simplify the exponents.
14 examples and their solutions.
am⋅an
Formula
am⋅an = am + n
Example
x6⋅x8
Solution x6⋅x8
= x6 + 8
= x14
= x6 + 8
= x14
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Example
32xy4⋅3x3y7
Solution 32 x y4⋅3 x3 y7
= 32 + 1⋅x1 + 3⋅y4 + 7
= 33⋅x4⋅y11
= 27x4y11
= 32 + 1⋅x1 + 3⋅y4 + 7
= 33⋅x4⋅y11
= 27x4y11
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(am)n
Formula
(am)n = am⋅n
Example
(x2)3
Solution (x2)3
= x2⋅3
= x6
= x2⋅3
= x6
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Example
((x4)2)5
Solution ((x4)2)5
= (x4⋅2)5
= (x8)5
= x8⋅5
= x40
= (x4⋅2)5
= (x8)5
= x8⋅5
= x40
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(ab)m
Formula
(ab)m = am⋅bm
Example
(x3y)2
Solution (x3y)2
= (x3)2⋅y2
= x6y2
= (x3)2⋅y2
= x6y2
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aman
Formula
aman = am - n
Example
x8x3 = ? (x ≠ 0)
Solution x8x3
= x8 - 3
= x5
= x8 - 3
= x5
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Example
12x7y2z94x4y2z5 = ? (x, y, z ≠ 0)
Solution 12 x7 y2 z94 x4 y2 z5
= 3⋅x7 - 4⋅z9 - 5
= 3x3z4
= 3⋅x7 - 4⋅z9 - 5
= 3x3z4
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(ab)m
Formula
(ab)m = ambm
Example
(xy2)3 = ? (y ≠ 0)
Solution (xy2)3
= x2(y2)3
= x2y6
= x2(y2)3
= x2y6
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Example
(3x4y)2 = ? (x, y ≠ 0)
Solution (3x4y)2 ⋅ (y2x)3
= 32⋅(x4)2y2 ⋅ y323⋅x3
= 9⋅x8y2 ⋅ y38⋅x3
= 9x5y8
= 32⋅(x4)2y2 ⋅ y323⋅x3
= 9⋅x8y2 ⋅ y38⋅x3
= 9x5y8
Close
Zero Exponent
Formula
a0 = 1
Example
20
Solution 20 = 1
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Example
4x2y0⋅(-3xy)0 (x, y ≠ 0)
Solution 4x2 y0⋅(-3xy)0
= 4x2⋅1⋅1
= 4x2
= 4x2⋅1⋅1
= 4x2
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Negative Exponent
Formula
a-m = 1am
Example
x-4 (x ≠ 0)
Solution x-4 = 1x4
Close
Example
1x-3 = ? (x ≠ 0)
Solution 1x-3 = x31
= x3
= x3
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Example
x-5y7x2y-1 = ? (x, y ≠ 0)
Solution x-5 y7x2 y-1
= y7⋅y1x5⋅x2
= y7 + 1x5 + 2
= y8x7
= y7⋅y1x5⋅x2
= y7 + 1x5 + 2
= y8x7
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