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Exponents

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

This topic focuses on practicing operations with fractional exponents involving the factoring of square integer bases. Students learn to simplify expressions by breaking down the base into its prime factors before applying the fractional exponent. Problems involve common square integers like 16, 36, 25, 4, and 9, requiring students to factor these numbers down to their prime components and then apply the power of one-half to simplify the expression. The aim is to enhance students' understanding of exponents and factoring, fundamental skills in handling more complex algebraic expressions.

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 4 to the power of (1 over 2 )
a A LaTex expression showing (2 times 2 times 2) to the power of (1 over 2 )
b A LaTex expression showing (2 times 2 times 7) 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 13) to the power of (1 over 2 )
e A LaTex expression showing (2 times 2 times 11) to the power of (1 over 2 )
f A LaTex expression showing (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 9 to the power of (1 over 2 )
a A LaTex expression showing (3 times 3 times 11) to the power of (1 over 2 )
b A LaTex expression showing (3 times 3 times 3) to the power of (1 over 2 )
c A LaTex expression showing (3 times 3 times 5) to the power of (1 over 2 )
d A LaTex expression showing (3 times 3) to the power of (1 over 2 )
e A LaTex expression showing (3 times 3 times 7) to the power of (1 over 2 )
f A LaTex expression showing (3 times 3 times 13) to the power of (1 over 2 )
3
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 6 times 3) to the power of (1 over 2 )
b A LaTex expression showing (2 times 2 times 3 times 3 times 11) 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 2 times 3 times 3) 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 3 times 3 times 13) to the power of (1 over 2 )
4
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 2) to the power of (1 over 2 )
b A LaTex expression showing (2 times 2 times 2 times 2) to the power of (1 over 2 )
c A LaTex expression showing (2 times 2 times 2 times 2 times 13) to the power of (1 over 2 )
d A LaTex expression showing (2 times 2 times 2 times 2 times 5) to the power of (1 over 2 )
e A LaTex expression showing (2 times 2 times 2) to the power of (1 over 2 )
f A LaTex expression showing (2 times 2 times 4) to the power of (1 over 2 )
5
Factor the base number to make it easier to solve
A LaTex expression showing 25 to the power of (1 over 2 )
a A LaTex expression showing (2 times 5 times 5) to the power of (1 over 2 )
b A LaTex expression showing (5 times 5 times 13) to the power of (1 over 2 )
c A LaTex expression showing (5 times 5 times 11) to the power of (1 over 2 )
d A LaTex expression showing (5 times 5) to the power of (1 over 2 )
e A LaTex expression showing (5 times 5 times 7) to the power of (1 over 2 )
f A LaTex expression showing (5 times 5 times 5) to the power of (1 over 2 )