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Exponents - Negative Fractional Exponents with Non-Square Integer Base - Factored Exponent to Answer (Level 2)

This math topic focuses on calculating exponents with negative fractional powers applied to non-square integer bases. The problems explore converting products raised to negative fractional exponents into simplified radical forms. Each question provides a distinct numerical expression involving factored bases and asks to find the correct simplified form among multiple choices. The topic engages learners in understanding and manipulating complex exponents with a focus on how negative and fractional exponents affect the base numbers. This enhances comprehension of exponential rules and operations within algebra.

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

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

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Find the answer when this factored number is raised to its exponent

(2⋅2⋅2⋅3)(−13)(2 \cdot 2 \cdot 2 \cdot 3)^{(\frac{-1}{3})}

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

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Math worksheet on 'Exponents - Negative Fractional Exponents with Non-Square Integer Base - Factored Exponent to Answer (Level 2)'. Part of a broader unit on 'Exponents - Negative and Fractional Bases and Exponents' Learn online: app.mobius.academy/math/units/exponents_negative_and_fractional_bases_review/
1
Find the answer when this factored number is raised to its exponent
A LaTex expression showing (2 times 2 times 3 times 3 times 3) to the power of (-1 over 2 )
a A LaTex expression showing 1 over square root of 3
b A LaTex expression showing 1 over 6square root of 3
c A LaTex expression showing 1 over 6
d A LaTex expression showing 1 over 5square root of 3
e A LaTex expression showing 1 over 2square root of 3
f A LaTex expression showing 1 over 3square root of 3
2
Find the answer when this factored number is raised to its exponent
A LaTex expression showing (2 times 3 times 3 times 3) to the power of (-1 over 2 )
a A LaTex expression showing 1 over 4square root of 6
b A LaTex expression showing 1 over 3
c A LaTex expression showing 1 over square root of 6
d A LaTex expression showing 1 over 3square root of 6
e A LaTex expression showing 1 over 5square root of 6
f A LaTex expression showing 1 over 2square root of 6
3
Find the answer when this factored number is raised to its exponent
A LaTex expression showing (2 times 2 times 2 times 3 times 3) to the power of (-1 over 2 )
a A LaTex expression showing 1 over 2square root of 2
b A LaTex expression showing 1 over square root of 2
c A LaTex expression showing 1 over 6square root of 3
d A LaTex expression showing 1 over 6
e A LaTex expression showing 1 over 4square root of 2
f A LaTex expression showing 1 over 6square root of 2
4
Find the answer when this factored number is raised to its exponent
A LaTex expression showing (2 times 2 times 2 times 2 times 2) to the power of (-1 over 2 )
a A LaTex expression showing 1 over 2square root of 2
b A LaTex expression showing 1 over 4square root of 4
c A LaTex expression showing 1 over 3square root of 2
d A LaTex expression showing 1 over 4square root of 2
e A LaTex expression showing 1 over 4square root of 3
f A LaTex expression showing 1 over square root of 2
5
Find the answer when this factored number is raised to its exponent
A LaTex expression showing (3 times 3 times 3 times 5) to the power of (-1 over 3 )
a A LaTex expression showing 1 over 3
b A LaTex expression showing 1 over 43-th root of 5
c A LaTex expression showing 1 over 33-th root of 5
d A LaTex expression showing 1 over 33-th root of 4
e A LaTex expression showing 1 over 23-th root of 5
f A LaTex expression showing 1 over 3-th root of 5
6
Find the answer when this factored number is raised to its exponent
A LaTex expression showing (2 times 2 times 2 times 2 times 3 times 3) to the power of (-1 over 2 )
a A LaTex expression showing 1 over 3
b A LaTex expression showing 1 over 1
c A LaTex expression showing 1 over 12
d A LaTex expression showing 1 over 2
e A LaTex expression showing 1 over 12square root of 2
f A LaTex expression showing 1 over 12square root of 3
7
Find the answer when this factored number is raised to its exponent
A LaTex expression showing (2 times 2 times 2 times 2 times 2) to the power of (-1 over 3 )
a A LaTex expression showing 1 over 3-th root of 4
b A LaTex expression showing 1 over 23-th root of 4
c A LaTex expression showing 1 over 53-th root of 4
d A LaTex expression showing 1 over 33-th root of 4
e A LaTex expression showing 1 over 43-th root of 4
f A LaTex expression showing 1 over 2