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Simplify. Express your answer using positive exponents.\newlineq7q6⋅q−2\frac{q^7}{q^6 \cdot q^{-2}}

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Q. Simplify. Express your answer using positive exponents.\newlineq7q6⋅q−2\frac{q^7}{q^6 \cdot q^{-2}}
  1. Identify Operation for Exponents: Identify the operation needed for the exponents 77, 66, and −2-2. When dividing powers with the same base, we subtract the exponents in the denominator from the exponent in the numerator. When multiplying powers with the same base, we add the exponents.
  2. Simplify Denominator: Simplify the denominator q6⋅q−2q^6 \cdot q^{-2} by adding the exponents.\newlineq6⋅q−2=q6+(−2)=q4q^6 \cdot q^{-2} = q^{6 + (-2)} = q^4
  3. Divide Numerator: Divide the numerator by the simplified denominator.\newlineq7/q4q^7 / q^4\newlineWhen dividing powers with the same base, subtract the exponent in the denominator from the exponent in the numerator.\newlineq7/q4=q(7−4)=q3q^7 / q^4 = q^{(7 - 4)} = q^3

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