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Exponents

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

This math topic focuses on understanding and applying the concept of fractional exponents with integer bases. Students are required to identify the equivalent form of a given fractional exponent expression. The problems include finding what a fractional exponent represents, such as the cube root, square root, or fourth root of numbers like 125, 32, 27, 16, 36, and 81. Each question provides multiple choices with different root evaluations of the base number. This helps in building proficiency in interpreting and simplifying fractional exponent expressions.

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

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Exponents - Fractional Exponents with Integer Base - Explanation to Answer Worksheet

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Exponents - Fractional Exponents with Integer Base - Explanation to Answer
1
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 ) = 16 \\ 16 to the power of (1 over 2 ) = ?
a A LaTex expression showing 16
b A LaTex expression showing 5
c A LaTex expression showing 2-th root of 16
d A LaTex expression showing 1 over 2-th root of 16
e A LaTex expression showing 4
f A LaTex expression showing 3
2
Given the hint, what is the fractional exponent the same as?
A LaTex expression showing 27 to the power of (1 over 3 ) times 27 to the power of (1 over 3 ) times 27 to the power of (1 over 3 ) = 27 \\ 27 to the power of (1 over 3 ) = ?
a A LaTex expression showing 1 over 3-th root of 27
b A LaTex expression showing 4
c A LaTex expression showing 2
d A LaTex expression showing 3
e A LaTex expression showing 3-th root of 27
f A LaTex expression showing 27
3
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 ) = 125 \\ 125 to the power of (1 over 3 ) = ?
a A LaTex expression showing 4
b A LaTex expression showing 5
c A LaTex expression showing 3-th root of 125
d A LaTex expression showing 1 over 3-th root of 125
e A LaTex expression showing 125
f A LaTex expression showing 6
4
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 ) = 216 \\ 216 to the power of (1 over 3 ) = ?
a A LaTex expression showing 1 over 3-th root of 216
b A LaTex expression showing 5
c A LaTex expression showing 6
d A LaTex expression showing 3-th root of 216
e A LaTex expression showing 216
f A LaTex expression showing 7
5
Given the hint, what is the fractional exponent the same as?
A LaTex expression showing 25 to the power of (1 over 2 ) times 25 to the power of (1 over 2 ) = 25 \\ 25 to the power of (1 over 2 ) = ?
a A LaTex expression showing 2-th root of 25
b A LaTex expression showing 6
c A LaTex expression showing 5
d A LaTex expression showing 1 over 2-th root of 25
e A LaTex expression showing 4
f A LaTex expression showing 25
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 ) = 32 \\ 32 to the power of (1 over 5 ) = ?
a A LaTex expression showing 3
b A LaTex expression showing 2
c A LaTex expression showing 1 over 5-th root of 32
d A LaTex expression showing 5-th root of 32
e A LaTex expression showing 32
f A LaTex expression showing 1
7
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 ) = 36 \\ 36 to the power of (1 over 2 ) = ?
a A LaTex expression showing 1 over 2-th root of 36
b A LaTex expression showing 2-th root of 36
c A LaTex expression showing 7
d A LaTex expression showing 5
e A LaTex expression showing 6
f A LaTex expression showing 36
8
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 ) = 16 \\ 16 to the power of (1 over 4 ) = ?
a A LaTex expression showing 4-th root of 16
b A LaTex expression showing 1
c A LaTex expression showing 3
d A LaTex expression showing 1 over 4-th root of 16
e A LaTex expression showing 2
f A LaTex expression showing 16