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

This math topic focuses on fractional exponents, particularly with non-square integer bases and their simplification to radical forms. Students practice evaluating expressions where an integer base, expressed as a product of factors, is raised to a fractional power. The problems include finding simplified or radical forms of these expressions, enhancing skills in manipulating exponents and understanding root extraction. Each question provides multiple choices, testing comprehension in simplifying expressions involving powers and roots, essential concepts in higher-level algebra.

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

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

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Exponents - Fractional Exponents with Non-Square Integer Base - Factored Exponent to Answer
1
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 23-th root of 4
b A LaTex expression showing 2
c A LaTex expression showing 23-th root of 2
d A LaTex expression showing 3-th root of 4
e A LaTex expression showing 33-th root of 4
2
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 33-th root of 5
b A LaTex expression showing 33-th root of 3
c A LaTex expression showing 3-th root of 5
d A LaTex expression showing 23-th root of 5
e A LaTex expression showing 3
f A LaTex expression showing 33-th root of 2
3
Find the answer when this factored number is raised to its exponent
A LaTex expression showing (2 times 2 times 2 times 2 times 5) to the power of (1 over 2 )
a A LaTex expression showing 4square root of 5
b A LaTex expression showing 2square root of 5
c A LaTex expression showing 4
d A LaTex expression showing 5square root of 5
e A LaTex expression showing square root of 5
f A LaTex expression showing 4square root of 2
4
Find the answer when this factored number is raised to its exponent
A LaTex expression showing (2 times 3 times 3 times 3 times 3) to the power of (1 over 4 )
a A LaTex expression showing 34-th root of 3
b A LaTex expression showing 54-th root of 2
c A LaTex expression showing 4-th root of 2
d A LaTex expression showing 44-th root of 2
e A LaTex expression showing 34-th root of 2
f A LaTex expression showing 3
5
Find the answer when this factored number is raised to its exponent
A LaTex expression showing (2 times 2 times 2 times 3) to the power of (1 over 3 )
a A LaTex expression showing 43-th root of 3
b A LaTex expression showing 23-th root of 4
c A LaTex expression showing 23-th root of 2
d A LaTex expression showing 23-th root of 3
e A LaTex expression showing 2
f A LaTex expression showing 3-th root of 3
6
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 5square root of 6
b A LaTex expression showing 2square root of 6
c A LaTex expression showing square root of 6
d A LaTex expression showing 3square root of 2
e A LaTex expression showing 3square root of 6
f A LaTex expression showing 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 3) to the power of (1 over 2 )
a A LaTex expression showing 5square root of 3
b A LaTex expression showing square root of 3
c A LaTex expression showing 3square root of 3
d A LaTex expression showing 4square root of 3
e A LaTex expression showing 4square root of 4
f A LaTex expression showing 4square root of 2
8
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 2square root of 3
b A LaTex expression showing 3square root of 3
c A LaTex expression showing 6
d A LaTex expression showing square root of 3
e A LaTex expression showing 6square root of 3
f A LaTex expression showing 5square root of 3