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Exponents - Negative Bases and Exponents - Practice

31 Topics, 5 Skills

Negative Integer Multiplication - Many of Same Number

Topic 1

Negative Integer Multiplication - Many of Same Number

Topic 2

Negative Base Expanded

Topic 3

Negative Base Expanded

Topic 4

Negative Base

Topic 5

Negative Base

Topic 6

Negative Exponents

Topic 7

Negative One Exponents with Unit Fractional Base

Topic 8

Negative One Exponents with Fractional Base

Topic 9

Negative Fractional Exponents with Integer Base - Explanation to Radical

Topic 10

Negative Fractional Exponents with Integer Base - Explanation to Radical

Topic 11

Negative Fractional Exponents with Integer Base - Explanation to Answer

Topic 12

Negative Fractional Exponents with Integer Base - Explanation to Answer

Topic 13

Negative Fractional Exponents with Square Integer Base - Exponent to Factored Exponent

Topic 14

Negative Fractional Exponents with Square Integer Base - Exponent to Factored Exponent

Topic 15

Negative Fractional Exponents with Square Integer Base - Factored Exponent to Answer

Topic 16

Negative Fractional Exponents with Square Integer Base - Factored Exponent to Answer

Topic 17

Negative Fractional Exponents with Square Integer Base - Exponent to Radical

Topic 18

Negative Fractional Exponents with Square Integer Base - Exponent to Radical

Topic 19

Negative Fractional Exponents with Square Integer Base - Exponent to Answer

Topic 20

Negative Fractional Exponents with Square Integer Base - Exponent to Answer

Topic 21

Negative Fractional Exponents with Non-Square Integer Base - Exponent to Factored Exponent

Topic 22

Negative Fractional Exponents with Non-Square Integer Base - Exponent to Factored Exponent

Topic 23

Negative Fractional Exponents with Non-Square Integer Base - Factored Exponent to Answer

Topic 24

Negative Fractional Exponents with Non-Square Integer Base - Factored Exponent to Answer

Topic 25

Negative Fractional Exponents with Non-Square Integer Base - Exponent to Unsimplified Radical

Topic 26

Negative Fractional Exponents with Non-Square Integer Base - Exponent to Unsimplified Radical

Topic 27

Negative Fractional Exponents with Non-Square Integer Base - Exponent to Factored Radical

Topic 28

Negative Fractional Exponents with Non-Square Integer Base - Exponent to Factored Radical

Topic 29

Negative Fractional Exponents with Non-Square Integer Base - Exponent to Simplified Radical

Topic 30

Negative Fractional Exponents with Non-Square Integer Base - Exponent to Simplified Radical

Topic 31

Exponents - Negative Fractional Exponents with Integer Base - Explanation to Radical (Level 2)

Topic 11

This math topic focuses on understanding negative fractional exponents with integer bases and their equivalence to radical forms. Students are tested on their ability to express powers like \( b^{-\frac{m}{n}} \) in terms of radicals, which involves interpreting expressions such as taking roots or inverses of integers raised to fractional powers. Problems involve calculations with different integer bases like 16, 25, 81, 36, 32, 64, and 125 to determine the correct radical equivalent of each given negative fractional exponent expression.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Negative Fractional Exponents with Integer Base - Explanation to Radical

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Given the hint, what is the fractional exponent the same as?

9(−12)⋅9(−12)=199(−12)=?9^{(\frac{-1}{2})} \cdot 9^{(\frac{-1}{2})} = \frac{1}{9} \\ 9^{(\frac{-1}{2})} = ?