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Exponents

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

This math topic focuses on practicing the skill of simplifying expressions with fractional exponents by factoring the base number. It involves using fractional powers with non-square integer bases, aiming to make the expression easier to simplify based on prime factorization and exponent rules. The discussed problems involve factoring the base of the number before solving the fractional exponent, challenging the understanding of fundamental properties of exponents and prime factorization.

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 - Exponent to Factored Exponent Worksheet

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Exponents - Fractional Exponents with Non-Square Integer Base - Exponent to Factored Exponent
1
Factor the base number to make it easier to solve
A LaTex expression showing 80 to the power of (1 over 2 )
a A LaTex expression showing (2 times 2 times 2 times 2 times 2 times 5) to the power of (1 over 2 )
b A LaTex expression showing (2 times 2 times 2 times 2 times 5 times 11) to the power of (1 over 2 )
c A LaTex expression showing (2 times 4 times 2 times 5) to the power of (1 over 2 )
d A LaTex expression showing (2 times 2 times 2 times 2 times 5 times 13) to the power of (1 over 2 )
e A LaTex expression showing (2 times 2 times 2 times 2 times 3 times 5) to the power of (1 over 2 )
f A LaTex expression showing (2 times 2 times 2 times 2 times 5) to the power of (1 over 2 )
2
Factor the base number to make it easier to solve
A LaTex expression showing 12 to the power of (1 over 2 )
a A LaTex expression showing (2 times 2 times 3 times 13) to the power of (1 over 2 )
b A LaTex expression showing (2 times 2 times 3 times 11) to the power of (1 over 2 )
c A LaTex expression showing (2 times 2 times 3) to the power of (1 over 2 )
d A LaTex expression showing (2 times 2 times 3 times 5) to the power of (1 over 2 )
e A LaTex expression showing (2 times 2 times 3 times 7) to the power of (1 over 2 )
f A LaTex expression showing (2 times 2 times 3 times 3) to the power of (1 over 2 )
3
Factor the base number to make it easier to solve
A LaTex expression showing 24 to the power of (1 over 2 )
a A LaTex expression showing (2 times 2 times 2 times 2 times 3) to the power of (1 over 2 )
b A LaTex expression showing (2 times 2 times 2 times 3) to the power of (1 over 2 )
c A LaTex expression showing (2 times 2 times 2 times 3 times 3) to the power of (1 over 2 )
d A LaTex expression showing (2 times 2 times 2) to the power of (1 over 2 )
e A LaTex expression showing (2 times 2 times 2 times 3 times 13) to the power of (1 over 2 )
f A LaTex expression showing (2 times 2 times 6) to the power of (1 over 2 )
4
Factor the base number to make it easier to solve
A LaTex expression showing 144 to the power of (1 over 2 )
a A LaTex expression showing (2 times 2 times 2 times 2 times 3 times 3) to the power of (1 over 2 )
b A LaTex expression showing (2 times 2 times 2 times 2 times 9) to the power of (1 over 2 )
c A LaTex expression showing (2 times 2 times 2 times 3 times 3) to the power of (1 over 2 )
d A LaTex expression showing (2 times 2 times 4 times 3 times 3) to the power of (1 over 2 )
e A LaTex expression showing (2 times 2 times 2 times 2 times 2 times 3 times 3) to the power of (1 over 2 )
f A LaTex expression showing (2 times 2 times 2 times 2 times 3) to the power of (1 over 2 )
5
Factor the base number to make it easier to solve
A LaTex expression showing 180 to the power of (1 over 2 )
a A LaTex expression showing (2 times 2 times 3 times 5) to the power of (1 over 2 )
b A LaTex expression showing (2 times 3 times 3 times 5) to the power of (1 over 2 )
c A LaTex expression showing (2 times 2 times 9 times 5) to the power of (1 over 2 )
d A LaTex expression showing (2 times 2 times 3 times 15) to the power of (1 over 2 )
e A LaTex expression showing (2 times 2 times 3 times 3 times 5) to the power of (1 over 2 )
f A LaTex expression showing (2 times 2 times 2 times 3 times 3 times 5) to the power of (1 over 2 )
6
Factor the base number to make it easier to solve
A LaTex expression showing 32 to the power of (1 over 2 )
a A LaTex expression showing (2 times 2 times 2 times 2 times 2) to the power of (1 over 2 )
b A LaTex expression showing (2 times 2 times 2 times 4) to the power of (1 over 2 )
c A LaTex expression showing (2 times 2 times 2 times 2 times 2 times 7) to the power of (1 over 2 )
d A LaTex expression showing (2 times 2 times 4 times 2) to the power of (1 over 2 )
e A LaTex expression showing (2 times 2 times 2 times 2) to the power of (1 over 2 )
f A LaTex expression showing (2 times 2 times 2 times 2 times 2 times 2) to the power of (1 over 2 )
7
Factor the base number to make it easier to solve
A LaTex expression showing 16 to the power of (1 over 2 )
a A LaTex expression showing (2 times 2 times 2 times 2 times 5) to the power of (1 over 2 )
b A LaTex expression showing (2 times 2 times 2 times 2 times 7) to the power of (1 over 2 )
c A LaTex expression showing (2 times 2 times 2 times 2) to the power of (1 over 2 )
d A LaTex expression showing (2 times 2 times 2 times 2 times 2) to the power of (1 over 2 )
e A LaTex expression showing (2 times 2 times 2 times 2 times 11) to the power of (1 over 2 )
f A LaTex expression showing (2 times 4 times 2) to the power of (1 over 2 )
8
Factor the base number to make it easier to solve
A LaTex expression showing 48 to the power of (1 over 2 )
a A LaTex expression showing (2 times 2 times 2 times 2 times 3 times 13) to the power of (1 over 2 )
b A LaTex expression showing (2 times 2 times 2 times 3) to the power of (1 over 2 )
c A LaTex expression showing (2 times 2 times 2 times 2) to the power of (1 over 2 )
d A LaTex expression showing (2 times 2 times 2 times 2 times 3 times 11) to the power of (1 over 2 )
e A LaTex expression showing (2 times 2 times 2 times 2 times 3) to the power of (1 over 2 )
f A LaTex expression showing (2 times 2 times 2 times 6) to the power of (1 over 2 )