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Simplify. Express your answer using positive exponents. \newline5k75k⋅k\frac{5k^7}{5k \cdot k}

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Multiply and divide powers: variable basesright chevron icon

Full solution

Q. Simplify. Express your answer using positive exponents. \newline5k75k⋅k\frac{5k^7}{5k \cdot k}
  1. Simplify denominator: Simplify the denominator 5k×k5k \times k. \newline5k×k=5k25k \times k = 5k^2
  2. Rewrite with simplified denominator: Rewrite the expression using the simplified denominator. 5k75k2\frac{5k^7}{5k^2}
  3. Apply quotient rule for exponents: Apply the quotient rule for exponents, am/an=a(m−n)a^m / a^n = a^{(m-n)}.\newline5k7/5k2=5(1−1)∗k(7−2)=50∗k5=1∗k5=k55k^7 / 5k^2 = 5^{(1-1)} * k^{(7-2)} = 5^0 * k^5 = 1 * k^5 = k^5

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