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Radicals - Convert Square Root, Values and Variables, to Exponents - Negative (Level 2)

This math topic focuses on converting radical notations into expressions with negative fractional exponents. It aims to strengthen the ability to simplify radicals by expressing them with exponents, especially at a more challenging level involving both numerical and variable components under the radical sign. The problems presented require a deep understanding of exponent rules and how to handle square roots of both constants and variables to transform them correctly into their equivalent exponential forms.

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

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Convert Square Root, Values and Variables, to Exponents - Negative

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Convert the radical to a fractional exponent

13rd5\frac{1}{\sqrt{3r{d}^{5}}}

Radicals - Convert Square Root, Values and Variables, to Exponents - Negative Worksheet

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Math worksheet on 'Radicals - Convert Square Root, Values and Variables, to Exponents - Negative (Level 2)'. Part of a broader unit on 'Radicals - Simplifying Practice' Learn online: app.mobius.academy/math/units/radicals_simplifying_practice/
1
Convert the radical to a fractional exponent
A LaTex expression showing 1 over square root of 7{b to the power of 3{x to the power of 5 }}
a A LaTex expression showing 7 to the power of 1 over 2 times {b} to the power of 3 over 2 times {x} to the power of 5 over 2
b A LaTex expression showing 7 to the power of -1 over 3 times {b} to the power of -3 over 3 times {x} to the power of -5 over 3
c A LaTex expression showing 7 to the power of -1 over 2 times {b} to the power of -2 over 2 times {x} to the power of -7 over 2
d A LaTex expression showing 7 to the power of -1 over 2 times {b} to the power of -3 over 2 times {x} to the power of -6 over 2
e A LaTex expression showing 7 to the power of -1 over 2 times {b} to the power of -3 over 2 times {x} to the power of -5 over 2
f A LaTex expression showing 7 to the power of -1 over 2 times {b} to the power of -5 over 2 times {x} to the power of -6 over 2
2
Convert the radical to a fractional exponent
A LaTex expression showing 1 over square root of 11{r to the power of 5{z to the power of 5 }}
a A LaTex expression showing 11 to the power of 1 over 2 times {r} to the power of 5 over 2 times {z} to the power of 5 over 2
b A LaTex expression showing 44 to the power of -1 over 2 times {r} to the power of -5 over 2 times {z} to the power of -5 over 2
c A LaTex expression showing 11 to the power of -1 over 3 times {r} to the power of -5 over 3 times {z} to the power of -5 over 3
d A LaTex expression showing 11 to the power of -1 over 2 times {r} to the power of -7 over 2 times {z} to the power of -4 over 2
e A LaTex expression showing 11 to the power of -1 over 2 times {r} to the power of -5 over 2 times {z} to the power of -5 over 2
f A LaTex expression showing 22 to the power of -1 over 2 times {r} to the power of -5 over 2 times {z} to the power of -5 over 2
3
Convert the radical to a fractional exponent
A LaTex expression showing 1 over square root of 11{m to the power of 5y }
a A LaTex expression showing 11 to the power of -1 over 2 times {m} to the power of -4 over 2 times {y} to the power of -2 over 2
b A LaTex expression showing 11 to the power of -1 over 2 times {m} to the power of -7 over 2 times
c A LaTex expression showing 11 to the power of -1 over 2 times {m} to the power of -5 over 2 times y to the power of -1 over 2
d A LaTex expression showing 11 to the power of 1 over 2 times {m} to the power of 5 over 2 times y to the power of 1 over 2
e A LaTex expression showing 11 to the power of -1 over 2 times {m} to the power of -4 over 2 times y to the power of -1 over 2
f A LaTex expression showing 44 to the power of -1 over 2 times {m} to the power of -5 over 2 times y to the power of -1 over 2
4
Convert the radical to a fractional exponent
A LaTex expression showing 1 over square root of 5{n to the power of 5c }
a A LaTex expression showing 10 to the power of -1 over 2 times {n} to the power of -5 over 2 times c to the power of -1 over 2
b A LaTex expression showing 5 to the power of -1 over 2 times {n} to the power of -5 over 2 times c to the power of -1 over 2
c A LaTex expression showing 15 to the power of -1 over 2 times {n} to the power of -5 over 2 times c to the power of -1 over 2
d A LaTex expression showing 5 to the power of -1 over 3 times {n} to the power of -5 over 3 times c to the power of -1 over 3
e A LaTex expression showing 20 to the power of -1 over 2 times {n} to the power of -5 over 2 times c to the power of -1 over 2
f A LaTex expression showing 5 to the power of 1 over 2 times {n} to the power of 5 over 2 times c to the power of 1 over 2
5
Convert the radical to a fractional exponent
A LaTex expression showing 1 over square root of 3d{n to the power of 5 }
a A LaTex expression showing 3 to the power of 1 over 2 times d to the power of 1 over 2 times {n} to the power of 5 over 2
b A LaTex expression showing 3 to the power of -1 over 2 times d to the power of -1 over 2 times {n} to the power of -7 over 2
c A LaTex expression showing 9 to the power of -1 over 2 times d to the power of -1 over 2 times {n} to the power of -5 over 2
d A LaTex expression showing 3 to the power of -1 over 2 times d to the power of -1 over 2 times {n} to the power of -5 over 2
e A LaTex expression showing 12 to the power of -1 over 2 times d to the power of -1 over 2 times {n} to the power of -5 over 2
f A LaTex expression showing 6 to the power of -1 over 2 times d to the power of -1 over 2 times {n} to the power of -5 over 2
6
Convert the radical to a fractional exponent
A LaTex expression showing 1 over square root of 5{m to the power of 5{n to the power of 5 }}
a A LaTex expression showing 5 to the power of -1 over 2 times {m} to the power of -7 over 2 times {n} to the power of -6 over 2
b A LaTex expression showing 5 to the power of -1 over 2 times {m} to the power of -5 over 2 times {n} to the power of -5 over 2
c A LaTex expression showing 5 to the power of -1 over 2 times {m} to the power of -6 over 2 times {n} to the power of -7 over 2
d A LaTex expression showing 5 to the power of -1 over 3 times {m} to the power of -5 over 3 times {n} to the power of -5 over 3
e A LaTex expression showing 5 to the power of 1 over 2 times {m} to the power of 5 over 2 times {n} to the power of 5 over 2
f A LaTex expression showing 5 to the power of -1 over 2 times {m} to the power of -5 over 2 times {n} to the power of -6 over 2
7
Convert the radical to a fractional exponent
A LaTex expression showing 1 over square root of 3r{d to the power of 5 }
a A LaTex expression showing 12 to the power of -1 over 2 times r to the power of -1 over 2 times {d} to the power of -5 over 2
b A LaTex expression showing 3 to the power of -1 over 2 times {r} to the power of -2 over 2 times {d} to the power of -6 over 2
c A LaTex expression showing 3 to the power of -1 over 2 times {r} to the power of -3 over 2 times {d} to the power of -6 over 2
d A LaTex expression showing 3 to the power of 1 over 2 times r to the power of 1 over 2 times {d} to the power of 5 over 2
e A LaTex expression showing 3 to the power of -1 over 2 times r to the power of -1 over 2 times {d} to the power of -5 over 2
f A LaTex expression showing 3 to the power of -1 over 3 times r to the power of -1 over 3 times {d} to the power of -5 over 3