9514 1404 393
Answer:
3^5
Step-by-step explanation:
It can be helpful to remember that <em>an exponent signifies repeated multiplication</em>.
The product in the numerator has 4 factors of 3 multiplied by 5 more factors of 3, for a total of 9 factors of 3.
The product in the denominator has 2 factors of 3 multiplied by 2 more factors of 3, for a total of 4 factors of 3.
The 4 factors of 3 in the denominator cancel 4 of the 9 factors of 3 in the numerator, leaving a value of 5 factors of 3.
The value of the expression is 3^5.
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In terms of rules of exponents, the value is ...
(3^4)(3^5)/((3^2)(3^2))
= 3^(4+5)/3^(2+2)
= 3^9/3^4
= 3^(9-4) = 3^5
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Those rules are ...
(a^b)(a^c) = a^(b+c)
(a^b)/(a^c) = a^(b-c)
