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Simplify using the laws of exponents, then evaluate     ((4^4m^3)/(3^3x^2))^4 x...

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aneeka101 | Student, Grade 11 | eNoter

Posted October 12, 2012 at 1:15 PM via web

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Simplify using the laws of exponents, then evaluate 

 

 ((4^4m^3)/(3^3x^2))^4 x ((3^2x^3)/(4^3m))^5

Everytime i try solving this equation, i get the wrong answer. please evaluate so i can compare it to my answer and see where i keep messing up 

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1 Answer | Add Yours

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samhouston | Middle School Teacher | (Level 1) Associate Educator

Posted October 12, 2012 at 1:59 PM (Answer #1)

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According to the laws of exponents:

  • (n^a) * (n^b) = n^(a + b)
  • (n^a) / (n^b) = n^(a - b)
  • (n^a)^b = n^(a*b)

Numerator of first fraction:  (4^4 * m^3)^4 = 4^16 * m^12

Denominator of first fraction:  (3^3 * x^2)^4 = 3^12 * x^8

Numerator of second fraction:  (3^2 * x^3)^5 = 3^10 * x^15

Denominator of second fraction:  (4^3 * m)^5 = 4^15 * m^5

You can cross simplify.

4^16 / 4^15 = 4

3^10 / 3^12 = 3^-2 = 1/9

m^12 / m^5 = m^7

x^15 / x^8 = x^7

Put it all together.

4/9 * m^7 * x^7 

 

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