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Exponents - Negative Fractional Exponents with Integer Base - Explanation to Answer (Level 1)

This math topic focuses on practicing how to handle negative fractional exponents with integer bases. Specifically, students interpret expressions like \( a^{-\frac{1}{2}} \times a^{-\frac{1}{2}} = \frac{1}{a} \), where 'a' is an integer, and determine the equivalent expression of a single exponent term. The exercises include identifying correct expressions among multiple choices for integer bases such as 36, 4, 9, 25, and 16 in relation to their negative fractional powers. This teaches the students about reciprocal and root operations with negative exponents in a simplified and concept-reinforcing manner.

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 Answer

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

16(−12)⋅16(−12)=11616(−12)=?16^{(\frac{-1}{2})} \cdot 16^{(\frac{-1}{2})} = \frac{1}{16} \\ 16^{(\frac{-1}{2})} = ?

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

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Math worksheet on 'Exponents - Negative Fractional Exponents with Integer Base - Explanation to Answer (Level 1)'. 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 25 to the power of (-1 over 2 ) times 25 to the power of (-1 over 2 ) = 1 over 25 \\ 25 to the power of (-1 over 2 ) = ?
a A LaTex expression showing 1 over 25 to the power of 2
b A LaTex expression showing 1 over 5
c A LaTex expression showing 3-th root of 25
d A LaTex expression showing 1 over 5 to the power of 2
e A LaTex expression showing 1 over 4
f A LaTex expression showing 1 over 6
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 36 to the power of 2
b A LaTex expression showing 1 over 6 to the power of 2
c A LaTex expression showing 1 over 5
d A LaTex expression showing 1 over 7
e A LaTex expression showing 3-th root of 36
f A LaTex expression showing 1 over 6
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 1
b A LaTex expression showing 3-th root of 4
c A LaTex expression showing 1 over 2
d A LaTex expression showing 1 over 2 to the power of 2
e A LaTex expression showing 1 over 4 to the power of 2
f A LaTex expression showing 1 over 3
4
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 4
b A LaTex expression showing 1 over 4 to the power of 2
c A LaTex expression showing 1 over 3
d A LaTex expression showing 1 over 5
e A LaTex expression showing 3-th root of 16
f A LaTex expression showing 1 over 16 to the power of 2
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 3-th root of 9
b A LaTex expression showing 1 over 3 to the power of 2
c A LaTex expression showing 1 over 3
d A LaTex expression showing 1 over 4
e A LaTex expression showing 1 over 2
f A LaTex expression showing 1 over 9 to the power of 2