Exponent

Negative Fractional Exponents with Square Integer Base - Exponent to Factored Exponent (Level 1)

This math topic focuses on the simplification of negative fractional exponents with square integer bases. Students practice factoring bases and applying negative fractional exponents to them. It includes problems revolving around integer bases like 36, 25, 16, 9, and 4, which are processed with exponents like -1/2. Students aim to factorize these bases and express them in exponent form to simplify the expressions effectively. A range of possible factorizations and simplifications provides multiple-choice answers, where students need to select the correct simplified form.

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

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Negative Fractional Exponents with Square Integer Base - Exponent to Factored Exponent

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Factor the base number and simplify to make it easier to solve

9^{(\frac{-1}{2})}

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Teaching Transcript

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Let's simplify this negative fractional exponent, 200 to the power of negative one half

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A negative exponent means 1 over the positive of that exponent, so we can rewrite this as 1 over 200 to the power of one half

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A fractional exponent is the same as a root of the same order as the denominator, so we can rewrite as 1 over the square root of 200

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Now let's factor the radical. 200 is 2 times 2 times 2 times 5 times 5

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We have a squared 2 and a squared 5 that we can remove, so our final answer becomes 1 over 10 root 2

Exponents - Negative Fractional Exponents with Square Integer Base - Exponent to Factored Exponent Worksheet

Math worksheet on 'Exponents - Negative Fractional Exponents with Square Integer Base - Exponent to Factored Exponent (Level 1)'. Part of a broader unit on 'Exponents - Fractional Bases and Exponents - Practice' Learn online: app.mobius.academy/math/units/exponents_fractional_bases_and_exponents_practice/

Factor the base number and simplify to make it easier to solve

A LaTex expression showing 25 to the power of (-1 over 2 )

a $A LaTex expression showing 1 over (5 times 5 times 13) to the power of (\frac{1 {2 )}}$

b $A LaTex expression showing 1 over (5 times 5 times 7) to the power of (\frac{1 {2 )}}$

c $A LaTex expression showing 1 over (5 times 5 times 11) to the power of (\frac{1 {2 )}}$

d $A LaTex expression showing 1 over (5 times 5) to the power of (\frac{1 {2 )}}$

e $A LaTex expression showing 1 over (3 times 5 times 5) to the power of (\frac{1 {2 )}}$

f $A LaTex expression showing 1 over (5 times 5 times 5) to the power of (\frac{1 {2 )}}$

Factor the base number and simplify to make it easier to solve

A LaTex expression showing 36 to the power of (-1 over 2 )

a $A LaTex expression showing 1 over (2 times 3 times 3) to the power of (\frac{1 {2 )}}$

b $A LaTex expression showing 1 over (2 times 2 times 3) to the power of (\frac{1 {2 )}}$

c $A LaTex expression showing 1 over (2 times 2 times 3 times 3) to the power of (\frac{1 {2 )}}$

d $A LaTex expression showing 1 over (2 times 2 times 9) to the power of (\frac{1 {2 )}}$

e $A LaTex expression showing 1 over (2 times 2 times 3 times 3 times 11) to the power of (\frac{1 {2 )}}$

f $A LaTex expression showing 1 over (2 times 2 times 2 times 3 times 3) to the power of (\frac{1 {2 )}}$

Factor the base number and simplify to make it easier to solve

A LaTex expression showing 16 to the power of (-1 over 2 )

a $A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 3) to the power of (\frac{1 {2 )}}$

b $A LaTex expression showing 1 over (2 times 2 times 4) to the power of (\frac{1 {2 )}}$

c $A LaTex expression showing 1 over (2 times 2 times 2 times 2) to the power of (\frac{1 {2 )}}$

d $A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 2) to the power of (\frac{1 {2 )}}$

e $A LaTex expression showing 1 over (2 times 2 times 2) to the power of (\frac{1 {2 )}}$

f $A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 5) to the power of (\frac{1 {2 )}}$

Factor the base number and simplify to make it easier to solve

A LaTex expression showing 4 to the power of (-1 over 2 )

a $A LaTex expression showing 1 over (2 times 2) to the power of (\frac{1 {2 )}}$

b $A LaTex expression showing 1 over (2 times 2 times 5) to the power of (\frac{1 {2 )}}$

c $A LaTex expression showing 1 over (2 times 2 times 2) to the power of (\frac{1 {2 )}}$

d $A LaTex expression showing 1 over (2 times 2 times 7) to the power of (\frac{1 {2 )}}$

e $A LaTex expression showing 1 over (2 times 2 times 11) to the power of (\frac{1 {2 )}}$

f $A LaTex expression showing 1 over (2 times 2 times 13) to the power of (\frac{1 {2 )}}$

Factor the base number and simplify to make it easier to solve

A LaTex expression showing 9 to the power of (-1 over 2 )

a $A LaTex expression showing 1 over (3 times 3 times 7) to the power of (\frac{1 {2 )}}$

b $A LaTex expression showing 1 over (3 times 3 times 13) to the power of (\frac{1 {2 )}}$

c $A LaTex expression showing 1 over (3 times 3 times 3) to the power of (\frac{1 {2 )}}$

d $A LaTex expression showing 1 over (3 times 3 times 11) to the power of (\frac{1 {2 )}}$

e $A LaTex expression showing 1 over (3 times 3 times 5) to the power of (\frac{1 {2 )}}$

f $A LaTex expression showing 1 over (3 times 3) to the power of (\frac{1 {2 )}}$

Exponent

Practice:

Negative Fractional Exponents with Square Integer Base - Exponent to Factored Exponent

Exponents - Negative Fractional Exponents with Square Integer Base - Exponent to Factored Exponent Worksheet