Convert Square Root, Values and Variables, to Exponents - Positive (Level 1)

This math topic focuses on the practice of converting radicals into their equivalent expressions with fractional exponents. Specifically, it involves transforming various square roots of numerical and algebraic expressions into power forms with positive fractional exponents. The problems cover a range of values and variables, ensuring the practice of converting both simple numbers and more complex expressions involving variables. This skill is a foundational aspect of simplifying radicals, preparing students for more advanced operations in algebra.

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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Radicals - Convert Square Root, Values and Variables, to Exponents - Positive
1
Convert the radical to a fractional exponent
A LaTex expression showing square root of 2p
a A LaTex expression showing 4 to the power of 1 over 2 times p to the power of 1 over 2
b A LaTex expression showing 2 to the power of 1 over 2 times p to the power of 1 over 2
c A LaTex expression showing 2 to the power of 1 over 2 times {p} to the power of 2 over 2
d A LaTex expression showing 2 to the power of -1 over 2 times p to the power of -1 over 2
2
Convert the radical to a fractional exponent
A LaTex expression showing square root of 2{d 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
b A LaTex expression showing 8 to the power of 1 over 2 times {d} 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
3
Convert the radical to a fractional exponent
A LaTex expression showing square root of 2{c to the power of 3 }
a A LaTex expression showing 4 to the power of 1 over 2 times {c} to the power of 3 over 2
b A LaTex expression showing 2 to the power of -1 over 2 times {c} to the power of -3 over 2
c A LaTex expression showing 2 to the power of 1 over 2 times {c} to the power of 4 over 2
d A LaTex expression showing 6 to the power of 1 over 2 times {c} to the power of 3 over 2
e A LaTex expression showing 2 to the power of 1 over 2 times {c} to the power of 3 over 2
4
Convert the radical to a fractional exponent
A LaTex expression showing square root of 7{p to the power of 3 }
a A LaTex expression showing 14 to the power of 1 over 2 times {p} to the power of 3 over 2
b A LaTex expression showing 7 to the power of 1 over 2 times {p} to the power of 3 over 2
c A LaTex expression showing 7 to the power of 1 over 3 times {p} to the power of 3 over 3
d A LaTex expression showing 21 to the power of 1 over 2 times {p} to the power of 3 over 2
e A LaTex expression showing 7 to the power of 1 over 2 times {p} to the power of 4 over 2
5
Convert the radical to a fractional exponent
A LaTex expression showing square root of 3{c to the power of 3 }
a A LaTex expression showing 9 to the power of 1 over 2 times {c} to the power of 3 over 2
b A LaTex expression showing 6 to the power of 1 over 2 times {c} to the power of 3 over 2
c A LaTex expression showing 3 to the power of 1 over 2 times {c} to the power of 4 over 2
d A LaTex expression showing 3 to the power of 1 over 2 times {c} to the power of 3 over 2
e A LaTex expression showing 12 to the power of 1 over 2 times {c} to the power of 3 over 2
6
Convert the radical to a fractional exponent
A LaTex expression showing square root of 2{x to the power of 3 }
a A LaTex expression showing 2 to the power of -1 over 2 times {x} to the power of -3 over 2
b A LaTex expression showing 2 to the power of 1 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 {x} to the power of 4 over 2
d A LaTex expression showing 2 to the power of 1 over 3 times {x} to the power of 3 over 3
e A LaTex expression showing 4 to the power of 1 over 2 times {x} to the power of 3 over 2
7
Convert the radical to a fractional exponent
A LaTex expression showing square root of 2{p to the power of 3 }
a A LaTex expression showing 4 to the power of 1 over 2 times {p} to the power of 3 over 2
b A LaTex expression showing 2 to the power of 1 over 2 times {p} to the power of 3 over 2
c A LaTex expression showing 2 to the power of 1 over 3 times {p} to the power of 3 over 3
d A LaTex expression showing 8 to the power of 1 over 2 times {p} to the power of 3 over 2
8
Convert the radical to a fractional exponent
A LaTex expression showing square root of 2{b to the power of 3 }
a A LaTex expression showing 2 to the power of 1 over 2 times {b} to the power of 3 over 2
b A LaTex expression showing 2 to the power of 1 over 3 times {b} to the power of 3 over 3
c A LaTex expression showing 2 to the power of -1 over 2 times {b} to the power of -3 over 2
d A LaTex expression showing 6 to the power of 1 over 2 times {b} to the power of 3 over 2