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

This math topic focuses on the practice of simplifying negative fractional exponents with non-square integer bases into radical expressions with factored bases. The problems involve converting expressions like those raised to the power of \(-\frac{1}{2}\) or \(-\frac{1}{3}\) into their radical counterparts, making sure to factorize the base correctly and then express them in radical form. It includes multiple choices for each expression, allowing users to select the correct factorization and radical representation. The topic falls under a broader unit of negative bases and exponents practice.

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

more
View

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

Mobius Math Academy logo
Exponents - Negative Fractional Exponents with Non-Square Integer Base - Exponent to Factored Radical
1
Factor this exponent's base number and express it as a radical
A LaTex expression showing 80 to the power of (-1 over 2 )
a A LaTex expression showing 1 over square root of 2 times 4 times 2 times 5
b A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2 times 2 times 5
c A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2 times 5
d A LaTex expression showing 1 over square root of 2 times 2 times 2 times 10
e A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2
f A LaTex expression showing 1 over square root of 2 times 2 times 2 times 5
2
Factor this exponent's base number and express it as a radical
A LaTex expression showing 150 to the power of (-1 over 2 )
a A LaTex expression showing 1 over square root of 2 times 3 times 5 times 5
b A LaTex expression showing 1 over square root of 2 times 3 times 5 times 5 times 7
c A LaTex expression showing 1 over square root of 2 times 15 times 5
d A LaTex expression showing 1 over square root of 3 times 5 times 5
e A LaTex expression showing 1 over square root of 2 times 3 times 25
f A LaTex expression showing 1 over square root of 2 times 5 times 5
3
Factor this exponent's base number and express it as a radical
A LaTex expression showing 18 to the power of (-1 over 2 )
a A LaTex expression showing 1 over square root of 2 times 3 times 3 times 3
b A LaTex expression showing 1 over square root of 2 times 3 times 3 times 7
c A LaTex expression showing 1 over square root of 2 times 3 times 3 times 5
d A LaTex expression showing 1 over square root of 2 times 3 times 3 times 13
e A LaTex expression showing 1 over square root of 2 times 3 times 3
f A LaTex expression showing 1 over square root of 2 times 3 times 3 times 11
4
Factor this exponent's base number and express it as a radical
A LaTex expression showing 48 to the power of (-1 over 2 )
a A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2
b A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2 times 3 times 5
c A LaTex expression showing 1 over square root of 2 times 4 times 2 times 3
d A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2 times 3
e A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2 times 2 times 3
f A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2 times 3 times 13
5
Factor this exponent's base number and express it as a radical
A LaTex expression showing 40 to the power of (-1 over 3 )
a A LaTex expression showing 1 over 3-th root of 2 times 2 times 2 times 3 times 5
b A LaTex expression showing 1 over 3-th root of 2 times 4 times 5
c A LaTex expression showing 1 over 3-th root of 2 times 2 times 5
d A LaTex expression showing 1 over 3-th root of 2 times 2 times 10
e A LaTex expression showing 1 over 3-th root of 2 times 2 times 2 times 2 times 5
f A LaTex expression showing 1 over 3-th root of 2 times 2 times 2 times 5
6
Factor this exponent's base number and express it as a radical
A LaTex expression showing 50 to the power of (-1 over 2 )
a A LaTex expression showing 1 over square root of 2 times 5 times 5 times 13
b A LaTex expression showing 1 over square root of 2 times 2 times 5 times 5
c A LaTex expression showing 1 over square root of 2 times 5 times 5 times 5
d A LaTex expression showing 1 over square root of 2 times 5 times 5
e A LaTex expression showing 1 over square root of 2 times 5 times 5 times 7
f A LaTex expression showing 1 over square root of 2 times 5 times 5 times 11
7
Factor this exponent's base number and express it as a radical
A LaTex expression showing 48 to the power of (-1 over 4 )
a A LaTex expression showing 1 over 4-th root of 2 times 2 times 2 times 2 times 3
b A LaTex expression showing 1 over 4-th root of 2 times 2 times 2 times 2 times 3 times 7
c A LaTex expression showing 1 over 4-th root of 2 times 2 times 2 times 2 times 2 times 3
d A LaTex expression showing 1 over 4-th root of 2 times 2 times 2 times 3
e A LaTex expression showing 1 over 4-th root of 2 times 2 times 2 times 2 times 3 times 11
f A LaTex expression showing 1 over 4-th root of 2 times 2 times 2 times 2 times 3 times 3
8
Factor this exponent's base number and express it as a radical
A LaTex expression showing 24 to the power of (-1 over 2 )
a A LaTex expression showing 1 over square root of 2 times 2 times 3
b A LaTex expression showing 1 over square root of 2 times 2 times 2 times 3 times 13
c A LaTex expression showing 1 over square root of 2 times 2 times 6
d A LaTex expression showing 1 over square root of 2 times 2 times 2 times 3
e A LaTex expression showing 1 over square root of 2 times 2 times 2 times 3 times 7
f A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2 times 3