In algebra, the basic common laws of exponents play a vital role in exponential equations. We shall understand them here. The very first law is a number that is raised to an exponent and then raised to a new exponent, that’s the same as keeping the base and multiplying the exponents. We also have a law that deals with negative exponents, which creates a reciprocal a positive exponent. And we have exponents that are fractions, and we have that situation it’s like taking the denominator root at your base and raising to the numerator.
For example we have to solve, 3x^3+5=29. We shall recall- the inverse operations to isolate operations for the variable getting solved. Firstly we shall get rid of the 29 by subtracting 5 on both sides to simplify the left hand side, which will leave with 3 x^3= 24. Her we had the addition equation and we used the inverse operation, subtraction to get rid of the 5. On this side we have 3 times x cubed.
This is the mathematicsexample of a multiple equation and inverse of multiple equations is division. So we can divide both side by 3 , as 3 over 3 will be divided and will come to 1 , will be left with x^3 on left and 24 divided by 3 is 8 on the right hand side. In order to consider x here our first law reconsidering as x rose to the exponent, which rose to an exponent will be the product of the raised exponent to the new exponent.
Thus ultimately we have to take x^3and raise it to some number, so that we have x to the first power left over. We require some number times 3 which equals 1. That would just left x to the first. We also know that 3 times the third is one. Take x ^3 and raise to the 1/3 power, substituting both sides by 1/3 we get x equal to 2 as cube root of 8 is 2.
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