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Simplify. Express your answer using positive exponents.\newline10q5q⋅q3\frac{10q^5}{q \cdot q^3}

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Multiply and divide powers: variable basesright chevron icon

Full solution

Q. Simplify. Express your answer using positive exponents.\newline10q5q⋅q3\frac{10q^5}{q \cdot q^3}
  1. Identify Base and Exponents: Write down the expression and identify the base and exponents.\newlineWe have the expression 10q5q⋅q3\frac{10q^5}{q \cdot q^3}. Here, the base is qq, and we have exponents in the numerator and denominator.
  2. Apply Quotient Rule: Apply the quotient rule for exponents.\newlineThe quotient rule states that when we divide powers with the same base, we subtract the exponents. \newline10q5q⋅q3=10q5q4\frac{10q^5}{q \cdot q^3} = \frac{10q^5}{q^4} (since q⋅q3=q1+3=q4q \cdot q^3 = q^{1+3} = q^4)
  3. Simplify Expression: Simplify the expression using the quotient rule. \newline10q5q4=10q5−4=10q1=10q\frac{10q^5}{q^4} = 10q^{5-4} = 10q^1 = 10q

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