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

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

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

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

25(−12)⋅25(−12)=12525(−12)=?25^{(\frac{-1}{2})} \cdot 25^{(\frac{-1}{2})} = \frac{1}{25} \\ 25^{(\frac{-1}{2})} = ?

Exponents - Negative Fractional Exponents with Integer Base - Explanation to Radical Worksheet

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Math worksheet on 'Exponents - Negative Fractional Exponents with Integer Base - Explanation to Radical (Level 2)'. Part of a broader unit on 'Exponents - Negative Bases and Exponents - Practice' Learn online: app.mobius.academy/math/units/exponents_negative_bases_and_exponents_practice/
1
Given the hint, what is the fractional exponent the same as?
A LaTex expression showing 216 to the power of (-1 over 3 ) times 216 to the power of (-1 over 3 ) times 216 to the power of (-1 over 3 ) = 1 over 216 \\ 216 to the power of (-1 over 3 ) = ?
a A LaTex expression showing 1 over 1
b A LaTex expression showing 1 over 53-th root of 216
c A LaTex expression showing 3-th root of 216
d A LaTex expression showing 1 over 3-th root of 216
e A LaTex expression showing 1 over 3-th root of 216 to the power of 2
f A LaTex expression showing 1 over 33-th root of 216
2
Given the hint, what is the fractional exponent the same as?
A LaTex expression showing 16 to the power of (-1 over 4 ) times 16 to the power of (-1 over 4 ) times 16 to the power of (-1 over 4 ) times 16 to the power of (-1 over 4 ) = 1 over 16 \\ 16 to the power of (-1 over 4 ) = ?
a A LaTex expression showing 4-th root of 16 to the power of 4
b A LaTex expression showing 4-th root of 16
c A LaTex expression showing 1 over 24-th root of 16
d A LaTex expression showing 1 over 4-th root of 16
e A LaTex expression showing 1 over 1
f A LaTex expression showing 1 over 4-th root of 16 to the power of 2
3
Given the hint, what is the fractional exponent the same as?
A LaTex expression showing 4 to the power of (-1 over 2 ) times 4 to the power of (-1 over 2 ) = 1 over 4 \\ 4 to the power of (-1 over 2 ) = ?
a A LaTex expression showing 1 over square root of 4
b A LaTex expression showing 1 over 1
c A LaTex expression showing 1 over square root of 3
d A LaTex expression showing 1 over 3square root of 4
e A LaTex expression showing 1 over square root of 4 to the power of 2
f A LaTex expression showing 1 over 5square root of 4
4
Given the hint, what is the fractional exponent the same as?
A LaTex expression showing 125 to the power of (-1 over 3 ) times 125 to the power of (-1 over 3 ) times 125 to the power of (-1 over 3 ) = 1 over 125 \\ 125 to the power of (-1 over 3 ) = ?
a A LaTex expression showing 1 over 1
b A LaTex expression showing 1 over 53-th root of 125
c A LaTex expression showing 1 over 33-th root of 125
d A LaTex expression showing 1 over 23-th root of 125
e A LaTex expression showing 1 over 43-th root of 125
f A LaTex expression showing 1 over 3-th root of 125
5
Given the hint, what is the fractional exponent the same as?
A LaTex expression showing 9 to the power of (-1 over 2 ) times 9 to the power of (-1 over 2 ) = 1 over 9 \\ 9 to the power of (-1 over 2 ) = ?
a A LaTex expression showing 1 over square root of 4
b A LaTex expression showing 1 over square root of 9
c A LaTex expression showing 1 over 5square root of 9
d A LaTex expression showing 1 over 1
e A LaTex expression showing 1 over square root of 2
f A LaTex expression showing 1 over 4square root of 9
6
Given the hint, what is the fractional exponent the same as?
A LaTex expression showing 32 to the power of (-1 over 5 ) times 32 to the power of (-1 over 5 ) times 32 to the power of (-1 over 5 ) times 32 to the power of (-1 over 5 ) times 32 to the power of (-1 over 5 ) = 1 over 32 \\ 32 to the power of (-1 over 5 ) = ?
a A LaTex expression showing 1 over 1
b A LaTex expression showing 1 over 45-th root of 32
c A LaTex expression showing 1 over 5-th root of 2
d A LaTex expression showing 1 over 5-th root of 32
e A LaTex expression showing 1 over 55-th root of 32
f A LaTex expression showing 1 over 25-th root of 32
7
Given the hint, what is the fractional exponent the same as?
A LaTex expression showing 16 to the power of (-1 over 2 ) times 16 to the power of (-1 over 2 ) = 1 over 16 \\ 16 to the power of (-1 over 2 ) = ?
a A LaTex expression showing 1 over square root of 4
b A LaTex expression showing 1 over square root of 16
c A LaTex expression showing 1 over 4square root of 16
d A LaTex expression showing 1 over 5square root of 16
e A LaTex expression showing 1 over 1
f A LaTex expression showing 1 over square root of 16 to the power of 2