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

This math topic focuses on converting radicals into fractional exponents. Learners are presented with problems involving both numerical values and variables under square roots, which they must rewrite using fractional exponents. This skill is an integral part of simplifying radicals, and the problems escalate in difficulty through multiple questions and possible answers. The exercise strengthens understanding of how exponents and radicals are interrelated, aiding in algebraic manipulation and simplification tasks. Multiple choice answers associated with each problem allow for testing comprehension and mistakes in conversion.

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

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

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Math worksheet on 'Radicals - Convert Square Root, Values and Variables, to Exponents - Positive (Level 2)'. Part of a broader unit on 'Radicals - Simplifying Advanced' Learn online: app.mobius.academy/math/units/radicals_simplifying_advanced/
1
Convert the radical to a fractional exponent
A LaTex expression showing square root of 7{b to the power of 3 {x} to the power of 3 }
a A LaTex expression showing 21 to the power of 1 over 2 times {b} to the power of 3 over 2 times {x} to the power of 3 over 2
b A LaTex expression showing 14 to the power of 1 over 2 times {b} to the power of 3 over 2 times {x} to the power of 3 over 2
c 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 -3 over 2
d 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 3 over 3
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 3 over 2
2
Convert the radical to a fractional exponent
A LaTex expression showing square root of 2{x to the power of 3 {d} to the power of 5 }
a A LaTex expression showing 8 to the power of 1 over 2 times {x} to the power of 3 over 2 times {d} to the power of 5 over 2
b A LaTex expression showing 2 to the power of 1 over 2 times {x} to the power of 3 over 2 times {d} to the power of 5 over 2
c A LaTex expression showing 2 to the power of -1 over 2 times {x} to the power of -3 over 2 times {d} to the power of -5 over 2
d A LaTex expression showing 4 to the power of 1 over 2 times {x} to the power of 3 over 2 times {d} to the power of 5 over 2
e A LaTex expression showing 2 to the power of 1 over 3 times {x} to the power of 3 over 3 times {d} to the power of 5 over 3
3
Convert the radical to a fractional exponent
A LaTex expression showing square root of 7{d to the power of 3 {m} to the power of 3 }
a A LaTex expression showing 7 to the power of 1 over 2 times {d} to the power of 3 over 2 times {m} to the power of 3 over 2
b A LaTex expression showing 7 to the power of 1 over 3 times {d} to the power of 3 over 3 times {m} to the power of 3 over 3
c A LaTex expression showing 28 to the power of 1 over 2 times {d} to the power of 3 over 2 times {m} to the power of 3 over 2
d A LaTex expression showing 14 to the power of 1 over 2 times {d} to the power of 3 over 2 times {m} to the power of 3 over 2
4
Convert the radical to a fractional exponent
A LaTex expression showing square root of 2{r to the power of 5 {x} to the power of 3 }
a A LaTex expression showing 2 to the power of 1 over 3 times {r} to the power of 5 over 3 times {x} to the power of 3 over 3
b A LaTex expression showing 8 to the power of 1 over 2 times {r} to the power of 5 over 2 times {x} to the power of 3 over 2
c A LaTex expression showing 2 to the power of 1 over 2 times {r} to the power of 5 over 2 times {x} to the power of 3 over 2
d A LaTex expression showing 2 to the power of 1 over 2 times {r} to the power of 5 over 2 times {x} to the power of 2 over 2
5
Convert the radical to a fractional exponent
A LaTex expression showing square root of 11{x to the power of 3 {m} to the power of 5 }
a A LaTex expression showing 22 to the power of 1 over 2 times {x} to the power of 3 over 2 times {m} to the power of 5 over 2
b A LaTex expression showing 11 to the power of 1 over 2 times {x} to the power of 2 over 2 times {m} to the power of 6 over 2
c A LaTex expression showing 11 to the power of -1 over 2 times {x} to the power of -3 over 2 times {m} to the power of -5 over 2
d A LaTex expression showing 11 to the power of 1 over 2 times {x} to the power of 3 over 2 times {m} to the power of 5 over 2
6
Convert the radical to a fractional exponent
A LaTex expression showing square root of 2{c to the power of 5 {x} to the power of 5 }
a A LaTex expression showing 2 to the power of 1 over 2 times {c} to the power of 6 over 2 times {x} to the power of 7 over 2
b A LaTex expression showing 2 to the power of 1 over 2 times {c} to the power of 7 over 2 times {x} to the power of 7 over 2
c A LaTex expression showing 2 to the power of -1 over 2 times {c} to the power of -5 over 2 times {x} to the power of -5 over 2
d A LaTex expression showing 6 to the power of 1 over 2 times {c} to the power of 5 over 2 times {x} to the power of 5 over 2
e A LaTex expression showing 2 to the power of 1 over 2 times {c} to the power of 5 over 2 times {x} to the power of 5 over 2
7
Convert the radical to a fractional exponent
A LaTex expression showing square root of 2{d to the power of 3 {r} to the power of 3 }
a A LaTex expression showing 2 to the power of 1 over 2 times {d} to the power of 3 over 2 times {r} to the power of 3 over 2
b A LaTex expression showing 2 to the power of 1 over 2 times {d} to the power of 2 over 2 times {r} to the power of 3 over 2
c A LaTex expression showing 2 to the power of 1 over 2 times {d} to the power of 3 over 2 times {r} to the power of 4 over 2
d A LaTex expression showing 2 to the power of 1 over 3 times {d} to the power of 3 over 3 times {r} to the power of 3 over 3
e A LaTex expression showing 6 to the power of 1 over 2 times {d} to the power of 3 over 2 times {r} to the power of 3 over 2