## An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |

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Page 130

... " . 3. Find the -mth power of an . 4. Find the mth power of a- " . 5. Find the - mth power of a- " . Ans . am n Ans . a - mn Ans . a - mn ̧ Ans . amn . Root of a Monomial ;

... " . 3. Find the -mth power of an . 4. Find the mth power of a- " . 5. Find the - mth power of a- " . Ans . am n Ans . a - mn Ans . a - mn ̧ Ans . amn . Root of a Monomial ;

**imaginary**quantity . 6. Find 130 . ALGEBRA . SI [ CH . V. § I. Page 131

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**imaginary**quantity . 6. Find the 6th power of the 5th power of a3 b c2 . Ans . a90 630 € 60 . 7. Find the qth power of the -pth power of the mth power of a- " ̧ 8. Find the rth power of am b¬n co d . Ans . amn PI . Ans . amr b − nr cpr ... Page 132

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**imaginary**quantity . 198. Corollary . When the exponent of a letter is not exactly divisible by the exponent of the root to be extracted , a fractional exponent is obtained , which may consequently be used to represent the radical sign ... Page 159

... , whose fourth power divided by 4th of it , and 167 subtracted from the quotient , gives the . remainder 12000 ? Ans . 11 . Cases of

... , whose fourth power divided by 4th of it , and 167 subtracted from the quotient , gives the . remainder 12000 ? Ans . 11 . Cases of

**imaginary**Solution . 29. Some merchants engage in CH . V. V. ] 159 BINOMIAL EQUATIONS . Page 160

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**imaginary**? and why should the problem in this case be impossible ? Ans . When b > a2 , that is , when the product of the sum and difference is required to be greater than the square of a . required number is x , this product is Now if ...### Other editions - View all

### Common terms and phrases

126 become zero 3d root arithmetical progression coefficient commensurable roots common difference contained continued fraction continued product Corollary deficient terms denote derivative Divide dividend division equal roots equal to zero equation x² factor Find the 3d Find the 4th Find the continued Find the greatest Find the number Find the square Find the sum Free the equation Geometrical Progression given equation given number gives greatest common divisor Hence imaginary roots last term least common multiple letter logarithm monomials multiplied number of real number of terms polynomial positive roots preceding article Problem quantities in example quotient radical quantities ratio real roots reduced remainder required equation required number row of signs Scholium Second Degree Solution Solve the equation square root Sturm's Theorem subtracted Theorem unity unknown quan unknown quantity variable whence