Module 12: Rational Exponents
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| Write the expression in radical form 6^(3/2) | The denominator of 2 becomes the index. The numerator of 3 becomes the power which it is raised by. (√6)^3 Square root of 6 to the third power.
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| Write the expression in radical form 7^(4/3) | The denominator of 3 becomes the index. The numerator of 4 becomes the power by which its raised. (3√7)^4 Cube root of 7 raised to the 4th power
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| Write the expression in exponential form (√10)^3 Square root of 10 cubed | The understood index of 2 becomes the denominator. The numerator is 3 because the that is the power its raised to. 10^(3/2)
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| Write the expression in exponential form (3√6x)^4 Cube root of 6x raised to the fourth power | The index of 3 becomes the denominator. The numerator is 4 because the that is the power its raised to. (6x)^(4/3)
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| What is the Power Rule? | The Power Rule: (a^m)^n = a^mn
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| What is the Product Rule? | The Product Rule: (a^m)*(a^n) = a^m+n
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| What is the Quotient Rule? | The Quotient Rule: (a^m)/(a^n) = a^m-n
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| Simplify (-64)^(2/3) | Rewrite as cubed root of negative 64 squared. (3√-64)^2. Cube root the negative 64 leaving -4. (-4)^2. Then square the -4, giving the answer of 16.
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| Simplify (4√16x^2) Fourth root of 16x squared | Fourth root the 16 and pull out the 2. 2(4√x^2). Divide out the fourth root of x. 2x^(2/4). Simplify the 2/4 to 1/2. 2x^1/2. x^(1/2) is the square root of x. 2√x is the answer.
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| Simplify 6√x^3 Sixth root of x cubed | Divide out the index into the x cubed. x^(3/6). Simplify. x^(1/2). x^(1/2) = √x. The answer is √x.
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Review the information in the table. When you are ready to quiz yourself you can hide individual columns or the entire table. Then you can click on the empty cells to reveal the answer. Try to recall what will be displayed before clicking the empty cell.
To hide a column, click on the column name.
To hide the entire table, click on the "Hide All" button.
You may also shuffle the rows of the table by clicking on the "Shuffle" button.
Or sort by any of the columns using the down arrow next to any column heading.
If you know all the data on any row, you can temporarily remove it by tapping the trash can to the right of the row.
To hide a column, click on the column name.
To hide the entire table, click on the "Hide All" button.
You may also shuffle the rows of the table by clicking on the "Shuffle" button.
Or sort by any of the columns using the down arrow next to any column heading.
If you know all the data on any row, you can temporarily remove it by tapping the trash can to the right of the row.
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Created by:
Wicah1
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