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Exponent

Fractional Exponents with Integer Base - Explanation to Radical (Level 2)

The math topic focuses on understanding and applying the concept of fractional exponents with integer bases. It guides learners to interpret expressions like \(8^{1/3}\) and relate them to their equivalent radical forms, such as the cube root of 8. Each problem presents a numerical base raised to a fractional exponent and requires identifying the radical equivalent of the expression. This is practiced through a series of exercises that provide different integer bases and fractional exponents, enhancing the learner's proficiency in simplifying complex exponential expressions to their root forms.

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

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Fractional Exponents with Integer Base - Explanation to Radical

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

10

Given the hint, what is the fractional exponent the same as?

25(12)⋅25(12)=2525(12)=?25^{(\frac{1}{2})} \cdot 25^{(\frac{1}{2})} = 25 \\ 25^{(\frac{1}{2})} = ?

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Solution Transcript

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Exponents - Fractional Exponents with Integer Base - Explanation to Radical Worksheet

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Math worksheet on 'Exponents - Fractional Exponents with Integer Base - Explanation to Radical (Level 2)'. Part of a broader unit on 'Exponents - Fractional Bases and Exponents - Intro' Learn online: app.mobius.academy/math/units/exponents_fractional_bases_and_exponents_intro/
1
Given the hint, what is the fractional exponent the same as?
A LaTex expression showing 32 to the power of (1 over 5 ) times 32 to the power of (1 over 5 ) times 32 to the power of (1 over 5 ) times 32 to the power of (1 over 5 ) times 32 to the power of (1 over 5 ) = 32 \\ 32 to the power of (1 over 5 ) = ?
a A LaTex expression showing 45-th root of 32
b A LaTex expression showing 5-th root of 32
c A LaTex expression showing 1 over 5-th root of 32
d A LaTex expression showing 55-th root of 32
e A LaTex expression showing 1
f A LaTex expression showing 35-th root of 32
2
Given the hint, what is the fractional exponent the same as?
A LaTex expression showing 36 to the power of (1 over 2 ) times 36 to the power of (1 over 2 ) = 36 \\ 36 to the power of (1 over 2 ) = ?
a A LaTex expression showing square root of 36
b A LaTex expression showing 4square root of 36
c A LaTex expression showing 1
d A LaTex expression showing 2square root of 36
e A LaTex expression showing square root of 36 to the power of 2
f A LaTex expression showing 1 over square root of 36
3
Given the hint, what is the fractional exponent the same as?
A LaTex expression showing 16 to the power of (1 over 2 ) times 16 to the power of (1 over 2 ) = 16 \\ 16 to the power of (1 over 2 ) = ?
a A LaTex expression showing 1 over square root of 16
b A LaTex expression showing square root of 16
c A LaTex expression showing 1
d A LaTex expression showing 4square root of 16
e A LaTex expression showing 2square root of 16
f A LaTex expression showing square root of 4
4
Given the hint, what is the fractional exponent the same as?
A LaTex expression showing 25 to the power of (1 over 2 ) times 25 to the power of (1 over 2 ) = 25 \\ 25 to the power of (1 over 2 ) = ?
a A LaTex expression showing 5square root of 25
b A LaTex expression showing 4square root of 25
c A LaTex expression showing square root of 25
d A LaTex expression showing 1
e A LaTex expression showing 3square root of 25
f A LaTex expression showing 2square root of 25
5
Given the hint, what is the fractional exponent the same as?
A LaTex expression showing 27 to the power of (1 over 3 ) times 27 to the power of (1 over 3 ) times 27 to the power of (1 over 3 ) = 27 \\ 27 to the power of (1 over 3 ) = ?
a A LaTex expression showing 1 over 3-th root of 27
b A LaTex expression showing 3-th root of 27 to the power of 3
c A LaTex expression showing 3-th root of 27
d A LaTex expression showing 53-th root of 27
e A LaTex expression showing 33-th root of 27
f A LaTex expression showing 1
6
Given the hint, what is the fractional exponent the same as?
A LaTex expression showing 8 to the power of (1 over 3 ) times 8 to the power of (1 over 3 ) times 8 to the power of (1 over 3 ) = 8 \\ 8 to the power of (1 over 3 ) = ?
a A LaTex expression showing 3-th root of 8
b A LaTex expression showing 1
c A LaTex expression showing 53-th root of 8
d A LaTex expression showing 23-th root of 8
e A LaTex expression showing 3-th root of 2
f A LaTex expression showing 33-th root of 8
7
Given the hint, what is the fractional exponent the same as?
A LaTex expression showing 64 to the power of (1 over 3 ) times 64 to the power of (1 over 3 ) times 64 to the power of (1 over 3 ) = 64 \\ 64 to the power of (1 over 3 ) = ?
a A LaTex expression showing 3-th root of 64 to the power of 3
b A LaTex expression showing 23-th root of 64
c A LaTex expression showing 3-th root of 64
d A LaTex expression showing 33-th root of 64
e A LaTex expression showing 1
f A LaTex expression showing 1 over 3-th root of 64