multiplication property of exponents
a^x*a^y = a^x+y
The multiplication property of exponents is a rule in mathematics that states that when two or more exponential numbers with the same base are multiplied together, the powers can be added. More formally, if a and b are real numbers and m and n are positive integers, then:
a^m * a^n = a^(m+n)
or
a^(m+n) = a^m * a^n
This property is true for any positive real number a and any positive integers m and n. For example,
5^3 * 5^4 = 5^(3+4) = 5^7
or
(2/3)^2 * (2/3)^3 = (2/3)^(2+3) = (2/3)^5
This property makes it easier to simplify expressions involving exponential numbers with the same base. Instead of multiplying the numbers out and then raising the base to the resulting power, we can simply add the exponents and raise the base to the sum of the exponents.
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