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Simplify. Express your answer using positive exponents.\newline10b5b4\frac{10b}{5b^4}

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Q. Simplify. Express your answer using positive exponents.\newline10b5b4\frac{10b}{5b^4}
  1. Write Expression: Write down the given expression.\newlineThe given expression is 10b5b4\frac{10b}{5b^4}. We need to simplify this expression by dividing the coefficients and subtracting the exponents of like bases.
  2. Divide Coefficients: Divide the coefficients.\newlineDivide 1010 by 55 to get 22.\newline10/5=210 / 5 = 2
  3. Apply Quotient Rule: Apply the quotient rule for exponents.\newlineWhen dividing powers with the same base, subtract the exponents.\newlinebb4=b(14)=b3\frac{b}{b^4} = b^{(1-4)} = b^{-3}
  4. Combine Results: Combine the results from Step 22 and Step 33.\newlineThe simplified expression is 2b32 \cdot b^{-3}. However, the question prompt asks for positive exponents.
  5. Express Positive Exponent: Express the negative exponent as a positive exponent.\newlineTo express b3b^{-3} with a positive exponent, we write it as 1/b31/b^3.\newlineSo, 2×b3=2/b32 \times b^{-3} = 2/b^3

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