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

This math topic focuses on practicing negative fractional exponents with integer bases. Specifically, learners are challenged to express terms with negative fractional exponents as radicals. Questions require understanding and applying properties of negative fractional exponents such as \( a^{-\frac{1}{2}} \) and how they represent the reciprocal of the square root of \( a \). Each question provides multiple-choice responses involving the simplification of exponential expressions into radical form, assessing learners' abilities to manipulate and interpret expressions involving roots and radicals based on given hints and integer bases such as 25, 9, 36, 16, and 4.

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?

4(−12)⋅4(−12)=144(−12)=?4^{(\frac{-1}{2})} \cdot 4^{(\frac{-1}{2})} = \frac{1}{4} \\ 4^{(\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 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 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 4square root of 16
b A LaTex expression showing 1 over 1
c A LaTex expression showing 1 over square root of 16 to the power of 2
d A LaTex expression showing 1 over square root of 4
e A LaTex expression showing 1 over 5square root of 16
f A LaTex expression showing 1 over square root of 16
2
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 1 over 5square root of 4
c A LaTex expression showing 1 over 3square root of 4
d A LaTex expression showing 1 over square root of 3
e A LaTex expression showing 1 over square root of 4 to the power of 2
f A LaTex expression showing 1 over square root of 4
3
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 square root of 36
b A LaTex expression showing 1 over 3square root of 36
c A LaTex expression showing 1 over 1
d A LaTex expression showing 1 over 2square root of 36
e A LaTex expression showing 1 over square root of 36 to the power of 2
f A LaTex expression showing square root of 36
4
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 4square root of 9
b A LaTex expression showing 1 over 5square root of 9
c A LaTex expression showing 1 over 1
d A LaTex expression showing 1 over square root of 4
e A LaTex expression showing 1 over square root of 2
f A LaTex expression showing 1 over square root of 9
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 ) = 1 over 25 \\ 25 to the power of (-1 over 2 ) = ?
a A LaTex expression showing 1 over 3square root of 25
b A LaTex expression showing 1 over square root of 25
c A LaTex expression showing 1 over 2square root of 25
d A LaTex expression showing 1 over square root of 2
e A LaTex expression showing 1 over square root of 25 to the power of 2
f A LaTex expression showing 1 over 1