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The laws of exponents work the same with rational exponents, the difference being they use fractions not integers.

Q: How are the laws of rational exponents similar to laws of integer exponents?

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An integer exponent is the number of times that a number is multiplied by itself. For example: if the exponent of a is 3, then it represents the number a3 = a*a*a. The laws of exponents can be extended to arrive at definitions of negative exponents [a-3 = 1/a3] and fractional exponents [a1/3 is the cube or third root of a]. These definitions can be further extended to exponents that are irrational numbers, or even complex number.

Paranthisis Exponent Multiply Divide Add Subtract you use pemdas for instance (2/3 x 3/2)3 + 5 = 8

In the number x, with positive integer exponent a, a is the number of times that 1 (not the number itself) is multiplied by x. So, for example in the expression, 43 the exponent is 3 and the number represented is "1 is multiplied by 4 three times". If you multiply 4 by itself 3 times, you will get 4*4 (one time) * 4 (two times) *4 (three times) and that is NOT 43: it is just a wrong description.The laws of exponents are:xa * xb = xa+bxa / xb = xa-b(xa)b = xa*b(xy)a = xa * yaThe first three are used to extend the domain of exponents to negative integers and rational numbers. Exponents to irrational numbers are defined as limits of the exponents of the rational sequences converging to the irrational number.Finally, 00 is not defined (because it does not converge).

kahit ano sagot

That depends how you choose to number the laws.

Related questions

An integer exponent is a count of the number of times a particular number (the base) must be multiplied together. For example, for the base x, x^a means x*x*x*...*x where there are a lots of x in the multiplication. The definition is simple to understand for integer values of the exponent. This definition gives rise to the laws of exponents, and these allow this definition to be extended to the case where the exponents are negative, fractions, irrational and even complex numbers.

An integer exponent is the number of times that a number is multiplied by itself. For example: if the exponent of a is 3, then it represents the number a3 = a*a*a. The laws of exponents can be extended to arrive at definitions of negative exponents [a-3 = 1/a3] and fractional exponents [a1/3 is the cube or third root of a]. These definitions can be further extended to exponents that are irrational numbers, or even complex number.

Paranthisis Exponent Multiply Divide Add Subtract you use pemdas for instance (2/3 x 3/2)3 + 5 = 8

In the number x, with positive integer exponent a, a is the number of times that 1 (not the number itself) is multiplied by x. So, for example in the expression, 43 the exponent is 3 and the number represented is "1 is multiplied by 4 three times". If you multiply 4 by itself 3 times, you will get 4*4 (one time) * 4 (two times) *4 (three times) and that is NOT 43: it is just a wrong description.The laws of exponents are:xa * xb = xa+bxa / xb = xa-b(xa)b = xa*b(xy)a = xa * yaThe first three are used to extend the domain of exponents to negative integers and rational numbers. Exponents to irrational numbers are defined as limits of the exponents of the rational sequences converging to the irrational number.Finally, 00 is not defined (because it does not converge).

a2 X a6 = a8

kahit ano sagot

That depends how you choose to number the laws.

This is one of the laws of exponents, which states that xa * xb = x(a+b) The base is x, and the two powers (or exponents) are a and b.

the base and the laws of exponent

Convert all expressions to the same base.

Exponents are used in many different contexts and for different, though related, reasons. Exponents are used in scientific notation to represent very large and very small numbers. The main purpose it to strip the number of unnecessary detail and to reduce the risk of errors. Exponents are used in algebra and calculus to deal with exponential or power functions. Many laws in physics, for example, involve powers (positive, negative or fractional) of basic measures. Calculations based on these laws are simper if exponents are used.

Other state governments passed similar laws.