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Exponents

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

This math topic focuses on applying the concept of fractional exponents to integers that are factored into their prime components. It specifically emphasizes factoring square integer bases and then applying fractional exponents, enhancing comprehension in manipulating powers and roots with variable bases. The exercises feature multiple questions that require students to factorize base numbers like 36, 32, 9, 25, 125, 81, and 64, then calculate their values raised to fractional powers such as 1/2, 1/3, 1/4, and 1/5. Each problem provides a selection of answers, illustrating different possible factorizations and their outcomes when exponentiated fractionally.

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

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

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Exponents - Fractional Exponents with Square Integer Base - Exponent to Factored Exponent
1
Factor the base number to make it easier to solve
A LaTex expression showing 64 to the power of (1 over 3 )
a A LaTex expression showing (2 times 2 times 2 times 2 times 2) to the power of (1 over 3 )
b A LaTex expression showing (2 times 2 times 2 times 2 times 2 times 2 times 5) to the power of (1 over 3 )
c A LaTex expression showing (2 times 2 times 2 times 4 times 2) to the power of (1 over 3 )
d A LaTex expression showing (2 times 2 times 2 times 2 times 2 times 2 times 11) to the power of (1 over 3 )
e A LaTex expression showing (2 times 2 times 2 times 2 times 2 times 2 times 2) to the power of (1 over 3 )
f A LaTex expression showing (2 times 2 times 2 times 2 times 2 times 2) to the power of (1 over 3 )
2
Factor the base number to make it easier to solve
A LaTex expression showing 8 to the power of (1 over 3 )
a A LaTex expression showing (2 times 2 times 2 times 13) to the power of (1 over 3 )
b A LaTex expression showing (2 times 2 times 2) to the power of (1 over 3 )
c A LaTex expression showing (2 times 2 times 2 times 7) to the power of (1 over 3 )
d A LaTex expression showing (2 times 2 times 2 times 11) to the power of (1 over 3 )
e A LaTex expression showing (2 times 2 times 2 times 5) to the power of (1 over 3 )
f A LaTex expression showing (2 times 2 times 2 times 3) to the power of (1 over 3 )
3
Factor the base number to make it easier to solve
A LaTex expression showing 16 to the power of (1 over 4 )
a A LaTex expression showing (2 times 2 times 2 times 2) to the power of (1 over 4 )
b A LaTex expression showing (2 times 4 times 2) to the power of (1 over 4 )
c A LaTex expression showing (2 times 2 times 2) to the power of (1 over 4 )
d A LaTex expression showing (2 times 2 times 2 times 2 times 2) to the power of (1 over 4 )
e A LaTex expression showing (2 times 2 times 4) to the power of (1 over 4 )
f A LaTex expression showing (2 times 2 times 2 times 2 times 11) to the power of (1 over 4 )
4
Factor the base number to make it easier to solve
A LaTex expression showing 81 to the power of (1 over 4 )
a A LaTex expression showing (3 times 3 times 3) to the power of (1 over 4 )
b A LaTex expression showing (3 times 3 times 3 times 3 times 13) to the power of (1 over 4 )
c A LaTex expression showing (3 times 3 times 3 times 3) to the power of (1 over 4 )
d A LaTex expression showing (3 times 3 times 3 times 3 times 7) to the power of (1 over 4 )
e A LaTex expression showing (3 times 3 times 9) to the power of (1 over 4 )
f A LaTex expression showing (3 times 3 times 3 times 3 times 5) to the power of (1 over 4 )
5
Factor the base number to make it easier to solve
A LaTex expression showing 32 to the power of (1 over 5 )
a A LaTex expression showing (2 times 2 times 2 times 2 times 2 times 2) to the power of (1 over 5 )
b A LaTex expression showing (2 times 2 times 2 times 2 times 2) to the power of (1 over 5 )
c A LaTex expression showing (2 times 4 times 2 times 2) to the power of (1 over 5 )
d A LaTex expression showing (2 times 2 times 2 times 4) to the power of (1 over 5 )
e A LaTex expression showing (2 times 2 times 2 times 2) to the power of (1 over 5 )
f A LaTex expression showing (2 times 2 times 4 times 2) to the power of (1 over 5 )
6
Factor the base number to make it easier to solve
A LaTex expression showing 4 to the power of (1 over 2 )
a A LaTex expression showing (2 times 2 times 11) to the power of (1 over 2 )
b A LaTex expression showing (2 times 2 times 2) to the power of (1 over 2 )
c A LaTex expression showing (2 times 2) to the power of (1 over 2 )
d A LaTex expression showing (2 times 2 times 7) to the power of (1 over 2 )
e A LaTex expression showing (2 times 2 times 5) to the power of (1 over 2 )
f A LaTex expression showing (2 times 2 times 13) to the power of (1 over 2 )
7
Factor the base number to make it easier to solve
A LaTex expression showing 36 to the power of (1 over 2 )
a A LaTex expression showing (2 times 2 times 3 times 3 times 11) to the power of (1 over 2 )
b A LaTex expression showing (2 times 2 times 2 times 3 times 3) to the power of (1 over 2 )
c A LaTex expression showing (2 times 2 times 3 times 3) to the power of (1 over 2 )
d A LaTex expression showing (2 times 2 times 3 times 3 times 5) to the power of (1 over 2 )
e A LaTex expression showing (2 times 2 times 3 times 3 times 13) to the power of (1 over 2 )
f A LaTex expression showing (2 times 6 times 3) to the power of (1 over 2 )
8
Factor the base number to make it easier to solve
A LaTex expression showing 216 to the power of (1 over 3 )
a A LaTex expression showing (2 times 2 times 3 times 3 times 3) to the power of (1 over 3 )
b A LaTex expression showing (2 times 2 times 2 times 3 times 3 times 3 times 13) to the power of (1 over 3 )
c A LaTex expression showing (2 times 2 times 2 times 2 times 3 times 3 times 3) to the power of (1 over 3 )
d A LaTex expression showing (2 times 4 times 3 times 3 times 3) to the power of (1 over 3 )
e A LaTex expression showing (2 times 2 times 2 times 9 times 3) to the power of (1 over 3 )
f A LaTex expression showing (2 times 2 times 2 times 3 times 3 times 3) to the power of (1 over 3 )