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.

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

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Exponents - Negative Fractional Exponents with Integer Base - Explanation to Radical
1
Given the hint, what is the fractional exponent the same as?
A LaTex expression showing 64 to the power of (-1 over 3 ) times 64 to the power of (-1 over 3 ) times 64 to the power of (-1 over 3 ) = 1 over 64 \\ 64 to the power of (-1 over 3 ) = ?
a A LaTex expression showing 1 over 1
b A LaTex expression showing 1 over 3-th root of 64 to the power of 2
c A LaTex expression showing 3-th root of 64
d A LaTex expression showing 1 over 33-th root of 64
e A LaTex expression showing 1 over 23-th root of 64
f A LaTex expression showing 1 over 3-th root of 64
2
Given the hint, what is the fractional exponent the same as?
A LaTex expression showing 36 to the power of (-1 over 2 ) times 36 to the power of (-1 over 2 ) = 1 over 36 \\ 36 to the power of (-1 over 2 ) = ?
a A LaTex expression showing 1 over 3square root of 36
b A LaTex expression showing 1 over 1
c A LaTex expression showing 1 over square root of 36 to the power of 2
d A LaTex expression showing square root of 36
e A LaTex expression showing 1 over 2square root of 36
f A LaTex expression showing 1 over square root of 36
3
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 9
b A LaTex expression showing 1 over square root of 2
c A LaTex expression showing 1 over 4square root of 9
d A LaTex expression showing 1 over 1
e A LaTex expression showing 1 over 5square root of 9
f A LaTex expression showing 1 over square root of 4
4
Given the hint, what is the fractional exponent the same as?
A LaTex expression showing 81 to the power of (-1 over 4 ) times 81 to the power of (-1 over 4 ) times 81 to the power of (-1 over 4 ) times 81 to the power of (-1 over 4 ) = 1 over 81 \\ 81 to the power of (-1 over 4 ) = ?
a A LaTex expression showing 1 over 4-th root of 81 to the power of 2
b A LaTex expression showing 1 over 1
c A LaTex expression showing 1 over 34-th root of 81
d A LaTex expression showing 1 over 54-th root of 81
e A LaTex expression showing 1 over 4-th root of 81
f A LaTex expression showing 1 over 44-th root of 81
5
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 3-th root of 216
b A LaTex expression showing 1 over 1
c A LaTex expression showing 1 over 3-th root of 216 to the power of 2
d A LaTex expression showing 1 over 3-th root of 216
e A LaTex expression showing 1 over 53-th root of 216
f A LaTex expression showing 1 over 33-th root of 216
6
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 1 over 24-th root of 16
b A LaTex expression showing 1 over 4-th root of 16
c A LaTex expression showing 1 over 4-th root of 16 to the power of 2
d A LaTex expression showing 4-th root of 16
e A LaTex expression showing 4-th root of 16 to the power of 4
f A LaTex expression showing 1 over 1
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 5square root of 16
b A LaTex expression showing 1 over square root of 4
c A LaTex expression showing 1 over 4square root of 16
d A LaTex expression showing 1 over 1
e A LaTex expression showing 1 over square root of 16 to the power of 2
f A LaTex expression showing 1 over square root of 16
8
Given the hint, what is the fractional exponent the same as?
A LaTex expression showing 8 to the power of (-1 over 3 ) times 8 to the power of (-1 over 3 ) times 8 to the power of (-1 over 3 ) = 1 over 8 \\ 8 to the power of (-1 over 3 ) = ?
a A LaTex expression showing 1 over 3-th root of 8
b A LaTex expression showing 3-th root of 8
c A LaTex expression showing 1 over 3-th root of 8 to the power of 2
d A LaTex expression showing 1 over 43-th root of 8
e A LaTex expression showing 1 over 33-th root of 8
f A LaTex expression showing 1 over 1