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Mathematics
  1. a. Write an equivalent expression for ( 3 4 ) 3 ( 3 4 ) 2 ((3)/(4))^(3)*((3)/(4))^(2).
    b. Describe the Law of Exponent that you applied.
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a. By using the product rule of exponentiation, we can multiply the powers with the same base by adding the exponents. Therefore, we have:
( 3 4 ) 3 ( 3 4 ) 2 = ( 3 4 ) 3 + 2 = ( 3 4 ) 5 ((3)/(4))^(3)*((3)/(4))^(2)=((3)/(4))^(3+2)=((3)/(4))^(5)
So, an equivalent expression for ( 3 4 ) 3 ( 3 4 ) 2 ((3)/(4))^(3)*((3)/(4))^(2) is ( 3 4 ) 5 ((3)/(4))^(5).
b. The law of exponent that we applied here is the product rule, which states that when multiplying powers with the same base, we can add their exponents. Mathematically,
a m a n = a m + n . a^(m)*a^(n)=a^(m+n).
In this case, we used the product rule to simplify the multiplication of ( 3 4 ) 3 ((3)/(4))^(3) and ( 3 4 ) 2 ((3)/(4))^(2) by adding their exponents and getting ( 3 4 ) 5 ((3)/(4))^(5).
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