Exponents

Product Rule of Powers

100

2² x 2⁴ = ?

2²⁺⁴

=2⁶

200

4² x 4⁹ = ?

4²⁺⁹

=4¹¹

300

(3²9⁴)(3⁵9¹) = ?

3²⁺⁵9⁴⁺¹

=3⁷9⁵

=3¹⁷

400

(x²3¹)(x⁶3¹³) = ?

x²⁺⁶3¹⁺¹³

=x⁸3¹⁴

500

(16²³⁹4³⁵10⁴⁹)(16⁷⁴4²¹⁶10⁷⁹) = ?

16³¹³4²⁵¹10¹²⁸

=2¹⁷⁵⁴10¹²⁸

Quotient Rule of Powers

100

2⁶/2³ = ?

2³

200

6¹⁴/6⁶ = ?

6⁸

300

(3⁹7¹² / 3⁴7⁹)² = ?

3⁵7³

400

9²³3⁸14¹⁹ / 9⁸3²14⁹ = ?

9¹⁵3⁶14¹⁰

500

(21¹⁴⁹10²⁷31¹¹¹ / 21⁶¹10¹⁹31⁴⁹)¹⁴ = ?

21¹²³²10¹¹²31⁸⁶⁸

Negative Exponents

100

2^-2 = ?

1 / 2²

200

6^-3 = ?

1 / 6³

300

2²3^-4 = ?

2^{2 /} 3⁴

400

7^-26² / 2²3^-3 = ?

6²3³ / 7²2²

500

5^-13⁴7^-39³10^-3 / 11^-24^-3

3⁴9³11²4³ / 5¹7³10³

Properties of Exponents

100

2⁴2⁷ / 2⁵

2⁶

200

2⁰2⁴4^-9 / x^-2

2⁴x² / 4⁹

300

2⁶4^-2x^-3 / 2⁵4^-6x⁵

2¹4⁴ / x²

400

x^-9y²z^-5 / x²y^-7z⁶

y⁹ / x¹¹z¹¹

500

x^-21x⁴y¹¹y²z⁵ / x^-25y⁷z²z^-7

y⁶z² / x⁴²

Miscellaneous Power Rules

100

2⁰ / 2

1 / 2

200

7^-47⁵ / 7^-6

7⁷

300

4²¹x^-7 / 4²x^-8

4¹⁹x¹

400

z^-29x⁰x^-9y²¹ / z²³z^-50y³⁰

1 / z⁵²x⁹y⁹

500

x^-23x⁰y²¹y¹⁰z^-20 / x^-23y³¹z^-10z^-10

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