Linear Algebra Examples

Find the Domain x^0.3=-0.76
Step 1
Convert expressions with fractional exponents to radicals.
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Step 1.1
Change into a fraction.
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Step 1.1.1
Multiply by to remove the decimal.
Step 1.1.2
Multiply by .
Step 1.1.3
Cancel the common factor of and .
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Step 1.1.3.1
Rewrite as .
Step 1.1.3.2
Cancel the common factors.
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Step 1.1.3.2.1
Rewrite as .
Step 1.1.3.2.2
Cancel the common factor.
Step 1.1.3.2.3
Rewrite the expression.
Step 1.2
Apply the rule to rewrite the exponentiation as a radical.
Step 2
Set the radicand in greater than or equal to to find where the expression is defined.
Step 3
Solve for .
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Step 3.1
Take the specified root of both sides of the inequality to eliminate the exponent on the left side.
Step 3.2
Simplify the equation.
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Step 3.2.1
Simplify the left side.
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Step 3.2.1.1
Pull terms out from under the radical.
Step 3.2.2
Simplify the right side.
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Step 3.2.2.1
Simplify .
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Step 3.2.2.1.1
Rewrite as .
Step 3.2.2.1.2
Pull terms out from under the radical.
Step 4
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Step 5