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Simplify. Express your answer as a single term using exponents.\newline53135315\frac{531^3}{531^5}

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Full solution

Q. Simplify. Express your answer as a single term using exponents.\newline53135315\frac{531^3}{531^5}
  1. Identify base and exponents: Identify the base and the exponents in the expression. In 5313531^3, 531531 is the base raised to the exponent 33. In 5315531^5, 531531 is the base raised to the exponent 55.
  2. Apply quotient of powers property: Apply the quotient of powers property, which states am/an=a(m−n)a^m / a^n = a^{(m-n)}. Here, calculate 5313/5315=531(3−5)531^3 / 531^5 = 531^{(3-5)}.
  3. Perform subtraction in exponent: Perform the subtraction in the exponent: 3−5=−23 - 5 = -2. So, 5313/5315531^3 / 531^5 simplifies to 531−2531^{-2}.

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