Basic Math Examples

Solve for r 3=81*r^(10-1)
Step 1
Rewrite the equation as .
Step 2
Subtract from .
Step 3
Divide each term in by and simplify.
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Step 3.1
Divide each term in by .
Step 3.2
Simplify the left side.
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Step 3.2.1
Cancel the common factor of .
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Step 3.2.1.1
Cancel the common factor.
Step 3.2.1.2
Divide by .
Step 3.3
Simplify the right side.
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Step 3.3.1
Cancel the common factor of and .
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Step 3.3.1.1
Factor out of .
Step 3.3.1.2
Cancel the common factors.
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Step 3.3.1.2.1
Factor out of .
Step 3.3.1.2.2
Cancel the common factor.
Step 3.3.1.2.3
Rewrite the expression.
Step 4
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 5
Simplify .
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Step 5.1
Rewrite as .
Step 5.2
Rewrite as .
Step 5.3
Rewrite as .
Step 5.4
Rewrite as .
Step 5.5
Pull terms out from under the radical, assuming real numbers.
Step 5.6
Rewrite as .
Step 5.7
Any root of is .
Step 5.8
Multiply by .
Step 5.9
Combine and simplify the denominator.
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Step 5.9.1
Multiply by .
Step 5.9.2
Raise to the power of .
Step 5.9.3
Use the power rule to combine exponents.
Step 5.9.4
Add and .
Step 5.9.5
Rewrite as .
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Step 5.9.5.1
Use to rewrite as .
Step 5.9.5.2
Apply the power rule and multiply exponents, .
Step 5.9.5.3
Combine and .
Step 5.9.5.4
Cancel the common factor of .
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Step 5.9.5.4.1
Cancel the common factor.
Step 5.9.5.4.2
Rewrite the expression.
Step 5.9.5.5
Evaluate the exponent.
Step 5.10
Simplify the numerator.
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Step 5.10.1
Rewrite as .
Step 5.10.2
Raise to the power of .
Step 6
The result can be shown in multiple forms.
Exact Form:
Decimal Form: