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Simplify. Express your answer using positive exponents. \newline5n8(5n4)(n9)\frac{5n^8}{(5n^4)(n^9)}

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Full solution

Q. Simplify. Express your answer using positive exponents. \newline5n8(5n4)(n9)\frac{5n^8}{(5n^4)(n^9)}
  1. Write Expression & Identify Terms: Write down the given expression and identify the similar terms that can be simplified.\newlineThe given expression is 5n8(5n4)(n9)\frac{5n^8}{(5n^4)(n^9)}. We can simplify this by canceling out common factors and using the laws of exponents.
  2. Cancel Common Factor: Cancel out the common factor of 55 in the numerator and the denominator.5n8(5n4)(n9)=n8(n4)(n9)\frac{5n^8}{(5n^4)(n^9)} = \frac{n^8}{(n^4)(n^9)}
  3. Apply Exponent Laws: Use the laws of exponents to simplify the expression further.\newlineWhen dividing powers with the same base, we subtract the exponents.\newlinen8/(n4)(n9)=n(8−4)/(n9)=n4/n9n^8/(n^4)(n^9) = n^{(8-4)}/(n^9) = n^4/n^9
  4. Simplify Further: Continue using the laws of exponents to simplify the expression. n4/n9=n4−9=n−5n^4/n^9 = n^{4-9} = n^{-5}
  5. Express as Positive Exponent: Since the question prompt asks for positive exponents, express n−5n^{-5} as 1/n51/n^5.\newlinen−5=1/n5n^{-5} = 1/n^5

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