Six laws of exponents with example
Answers
laws of exponents :-
Reciprocal Law
Can that exponent be negative? The answer is yes. It means that when a number has a negative exponent, the given number is a decimal number. If we have a number with negative index, say a−n then we can represent it in terms of a positive index by taking its reciprocal. Thus
a−n = 1/an
Exponent with Fractional Index
Fractional Exponents also called Rational Exponents. In fractional exponent, the numerator is the power to which the number should be taken and the denominator is the root which should be taken.
x1/n = n√x and xm/n=n√xm
Product Law of Exponents
According to the product law of exponents when multiplying two numbers that have the same base then we can add the exponents, as
xm.xn = xm+n
Quotient Law of Exponents
According to the quotient law of exponents, we can divide two numbers with the same base by subtracting the exponents.
xm÷xn = xm-n
Power Law of Exponents
According to the power law of exponents if a number raise a power to a power, just multiply the exponents
(xm)n=xmn
Power of Product Rule
The power of product rule states that:
(a×b)n=an×bn
Power of Quotient Rule
The power of product rule states that:
(a/b)n=an/bn