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Exponents - Fractional Exponents with Integer Base - Explanation to Answer (Level 1)

This math topic deals with the concept of fractional exponents with integer bases. Students are required to identify what a given fractional exponent represents. It involves simplifying expressions such as figuring out what \( x^{1/2} \) equals when \( x \) is an integer. This involves understanding and applying the rules of radicals and exponents. The problems involve common bases like 4, 9, 16, 25, and 36, converting them through fractional exponents to derive specific integer or radical results. Each question offers multiple choices and requires the application of simplifying square roots.

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 Answer

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

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

25(12)â‹…25(12)=2525(12)=?25^{(\frac{1}{2})} \cdot 25^{(\frac{1}{2})} = 25 \\ 25^{(\frac{1}{2})} = ?

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

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Math worksheet on 'Exponents - Fractional Exponents with Integer Base - Explanation to Answer (Level 1)'. 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 9 to the power of (1 over 2 ) times 9 to the power of (1 over 2 ) = 9 \\ 9 to the power of (1 over 2 ) = ?
a A LaTex expression showing 4
b A LaTex expression showing 3
c A LaTex expression showing 9
d A LaTex expression showing 1 over 2-th root of 9
e A LaTex expression showing 2
f A LaTex expression showing 2-th root of 9
2
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 4
b A LaTex expression showing 2-th root of 25
c A LaTex expression showing 6
d A LaTex expression showing 1 over 2-th root of 25
e A LaTex expression showing 5
f A LaTex expression showing 25
3
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 5
b A LaTex expression showing 2-th root of 36
c A LaTex expression showing 6
d A LaTex expression showing 7
e A LaTex expression showing 36
f A LaTex expression showing 1 over 2-th root of 36
4
Given the hint, what is the fractional exponent the same as?
A LaTex expression showing 4 to the power of (1 over 2 ) times 4 to the power of (1 over 2 ) = 4 \\ 4 to the power of (1 over 2 ) = ?
a A LaTex expression showing 4
b A LaTex expression showing 3
c A LaTex expression showing 1
d A LaTex expression showing 2
e A LaTex expression showing 1 over 2-th root of 4
f A LaTex expression showing 2-th root of 4
5
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 3
b A LaTex expression showing 1 over 2-th root of 16
c A LaTex expression showing 16
d A LaTex expression showing 5
e A LaTex expression showing 2-th root of 16
f A LaTex expression showing 4