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Radicals

Convert Cube Root, Values and Variables, from Exponents - Negative (Level 1)

This math topic focuses on converting fractional exponents to radical forms, specifically dealing with negative exponents and cube roots. It practices simplifying complex expressions involving powers and roots of numerical values and variables. The problems involve interpreting expressions with negative fractional exponents and expressing them as radicals, aiding in developing skills in simplification and manipulation of exponent and radical expressions.

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

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Radicals - Convert Cube Root, Values and Variables, from Exponents - Negative Worksheet

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Radicals - Convert Cube Root, Values and Variables, from Exponents - Negative
1
Convert the fractional exponent to a radical
A LaTex expression showing 3 to the power of -1 over 3 times x to the power of -1 over 3
a A LaTex expression showing 43-th root of 5x
b A LaTex expression showing 1 over 43-th root of 5x
c A LaTex expression showing 1 over 43-th root of x
d A LaTex expression showing 1 over 3-th root of {x to the power of 3 }
e A LaTex expression showing 1 over 3-th root of 3x
2
Convert the fractional exponent to a radical
A LaTex expression showing 2 to the power of -1 over 3 times {x} to the power of -2 over 3
a A LaTex expression showing 1 over 3-th root of {x to the power of 4 }
b A LaTex expression showing 3-th root of x
c A LaTex expression showing 33-th root of 3{x to the power of 2 }
d A LaTex expression showing 1 over 3-th root of 2{x to the power of 2 }
e A LaTex expression showing 1 over 23-th root of x
3
Convert the fractional exponent to a radical
A LaTex expression showing 7 to the power of -1 over 3 times {n} to the power of -2 over 3
a A LaTex expression showing 1 over 3-th root of 7{n to the power of 3 }
b A LaTex expression showing 3-th root of 4{n to the power of 2 }
c A LaTex expression showing 3-th root of 6{n to the power of 2 }
d A LaTex expression showing 1 over 43-th root of 4{n to the power of 4 }
e A LaTex expression showing 1 over 3-th root of 7{n to the power of 2 }
4
Convert the fractional exponent to a radical
A LaTex expression showing 11 to the power of -1 over 3 times {d} to the power of -2 over 3
a A LaTex expression showing 1 over 33-th root of 12{d to the power of 4 }
b A LaTex expression showing 1 over 3-th root of 8d
c A LaTex expression showing 1 over 33-th root of 10d
d A LaTex expression showing 43-th root of 8d
e A LaTex expression showing 1 over 3-th root of 11{d to the power of 2 }
5
Convert the fractional exponent to a radical
A LaTex expression showing 5 to the power of -1 over 3 times {z} to the power of -2 over 3
a A LaTex expression showing 1 over 33-th root of 8z
b A LaTex expression showing 1 over 3-th root of 3z
c A LaTex expression showing 1 over 3-th root of 5{z to the power of 2 }
d A LaTex expression showing 1 over 43-th root of 6{z to the power of 2 }
e A LaTex expression showing 3-th root of 7z
6
Convert the fractional exponent to a radical
A LaTex expression showing 2 to the power of -1 over 3 times m to the power of -1 over 3
a A LaTex expression showing 1 over 3-th root of 2m
b A LaTex expression showing 3-th root of 4m
c A LaTex expression showing 1 over 3-th root of 2{m to the power of 3 }
d A LaTex expression showing 1 over 3-th root of 4m
e A LaTex expression showing 1 over 3-th root of m
7
Convert the fractional exponent to a radical
A LaTex expression showing 11 to the power of -1 over 3 times b to the power of -1 over 3
a A LaTex expression showing 1 over 23-th root of 10b
b A LaTex expression showing 1 over 43-th root of 12b
c A LaTex expression showing 1 over 3-th root of 11b
d A LaTex expression showing 1 over 3-th root of 12b
e A LaTex expression showing 3-th root of 13b
8
Convert the fractional exponent to a radical
A LaTex expression showing 2 to the power of -1 over 3 times z to the power of -1 over 3
a A LaTex expression showing 1 over 43-th root of {z to the power of 2 }
b A LaTex expression showing 1 over 23-th root of 5z
c A LaTex expression showing 1 over 23-th root of 2z
d A LaTex expression showing 1 over 3-th root of 2z
e A LaTex expression showing 33-th root of 4{z to the power of 2 }