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Exponents

Negative Fractional Exponents with Non-Square Integer Base - Exponent to Factored Radical (Level 1)

This math topic focuses on practicing how to work with negative fractional exponents involving non-square integer bases, specifically by factoring the base number and expressing the result as a radical. Each problem presents an integer raised to the power of a negative fractional exponent, and students are required to simplify these expressions by breaking down the base number into its prime factors and converting the exponentiation into a radical form. Multiple choice answers are provided for students to ascertain the correct simplified expression. This is part of a broader unit on negative bases and exponents.

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

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Exponents - Negative Fractional Exponents with Non-Square Integer Base - Exponent to Factored Radical Worksheet

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Exponents - Negative Fractional Exponents with Non-Square Integer Base - Exponent to Factored Radical
1
Factor this exponent's base number and express it as a radical
A LaTex expression showing 96 to the power of (-1 over 2 )
a A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2 times 2 times 3 times 3
b A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2 times 2 times 3
c A LaTex expression showing 1 over square root of 2 times 4 times 2 times 2 times 3
d A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2 times 2 times 2 times 3
e A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2 times 2 times 3 times 11
f A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2 times 3
2
Factor this exponent's base number and express it as a radical
A LaTex expression showing 100 to the power of (-1 over 2 )
a A LaTex expression showing 1 over square root of 2 times 2 times 2 times 5 times 5
b A LaTex expression showing 1 over square root of 2 times 5 times 5
c A LaTex expression showing 1 over square root of 2 times 2 times 5 times 5 times 11
d A LaTex expression showing 1 over square root of 2 times 2 times 5 times 5 times 7
e A LaTex expression showing 1 over square root of 2 times 2 times 5
f A LaTex expression showing 1 over square root of 2 times 2 times 5 times 5
3
Factor this exponent's base number and express it as a radical
A LaTex expression showing 50 to the power of (-1 over 2 )
a A LaTex expression showing 1 over square root of 2 times 2 times 5 times 5
b A LaTex expression showing 1 over square root of 2 times 5 times 5 times 13
c A LaTex expression showing 1 over square root of 2 times 5 times 5 times 7
d A LaTex expression showing 1 over square root of 2 times 5 times 5
e A LaTex expression showing 1 over square root of 2 times 5 times 5 times 5
f A LaTex expression showing 1 over square root of 2 times 5 times 5 times 11
4
Factor this exponent's base number and express it as a radical
A LaTex expression showing 45 to the power of (-1 over 2 )
a A LaTex expression showing 1 over square root of 3 times 3 times 5 times 11
b A LaTex expression showing 1 over square root of 2 times 3 times 3 times 5
c A LaTex expression showing 1 over square root of 3 times 3 times 3 times 5
d A LaTex expression showing 1 over square root of 3 times 3 times 5 times 13
e A LaTex expression showing 1 over square root of 3 times 3 times 5
f A LaTex expression showing 1 over square root of 3 times 3 times 5 times 5
5
Factor this exponent's base number and express it as a radical
A LaTex expression showing 180 to the power of (-1 over 2 )
a A LaTex expression showing 1 over square root of 2 times 2 times 3 times 3
b A LaTex expression showing 1 over square root of 2 times 6 times 3 times 5
c A LaTex expression showing 1 over square root of 2 times 2 times 3 times 3 times 5 times 5
d A LaTex expression showing 1 over square root of 2 times 2 times 3 times 15
e A LaTex expression showing 1 over square root of 2 times 2 times 3 times 3 times 5
f A LaTex expression showing 1 over square root of 2 times 2 times 3 times 3 times 5 times 11
6
Factor this exponent's base number and express it as a radical
A LaTex expression showing 16 to the power of (-1 over 2 )
a A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2 times 2
b A LaTex expression showing 1 over square root of 2 times 2 times 4
c A LaTex expression showing 1 over square root of 2 times 4 times 2
d A LaTex expression showing 1 over square root of 2 times 2 times 2
e A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2 times 7
f A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2
7
Factor this exponent's base number and express it as a radical
A LaTex expression showing 18 to the power of (-1 over 2 )
a A LaTex expression showing 1 over square root of 2 times 3 times 3 times 11
b A LaTex expression showing 1 over square root of 2 times 3 times 3 times 3
c A LaTex expression showing 1 over square root of 2 times 3 times 3 times 7
d A LaTex expression showing 1 over square root of 2 times 3 times 3 times 13
e A LaTex expression showing 1 over square root of 2 times 3 times 3
f A LaTex expression showing 1 over square root of 2 times 3 times 3 times 5
8
Factor this exponent's base number and express it as a radical
A LaTex expression showing 80 to the power of (-1 over 2 )
a A LaTex expression showing 1 over square root of 2 times 2 times 2 times 5
b A LaTex expression showing 1 over square root of 2 times 4 times 2 times 5
c A LaTex expression showing 1 over square root of 2 times 2 times 2 times 10
d A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2
e A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2 times 5
f A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2 times 2 times 5