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Simplify. Express your answer using positive exponents. \newline2b52b7\frac{2b^5}{2b^7}

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Full solution

Q. Simplify. Express your answer using positive exponents. \newline2b52b7\frac{2b^5}{2b^7}
  1. Apply quotient rule: Apply the quotient rule for exponents.\newlineThe quotient rule states that when dividing like bases with exponents, you subtract the exponents.\newline2b52b7=22×b(5−7)\frac{2b^5}{2b^7} = \frac{2}{2} \times b^{(5-7)}
  2. Simplify coefficients and exponents: Simplify the coefficients and the exponents. 22=1\frac{2}{2} = 1 and b(5−7)=b−2b^{(5-7)} = b^{-2} So, 2b52b7\frac{2b^5}{2b^7} simplifies to 1×b−21 \times b^{-2}
  3. Express answer with positive exponents: Express the answer using positive exponents.\newlineTo express b−2b^{-2} with a positive exponent, we write it as 1/b21/b^2.\newlineTherefore, the simplified expression is 1/b21/b^2.

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