Question

Solve the following problem:

Answer 1

9514 1404 393

Answer:

  3^5

Step-by-step explanation:

It can be helpful to remember that an exponent signifies repeated multiplication.

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)