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Simplify. Express your answer using positive exponents. \newlinek3k5k5\frac{k^3}{k^5 \cdot k^5}

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Q. Simplify. Express your answer using positive exponents. \newlinek3k5k5\frac{k^3}{k^5 \cdot k^5}
  1. Identify Operation: Identify the operation needed for the exponents.\newlineWhen dividing powers with the same base, we subtract the exponents. When multiplying powers with the same base, we add the exponents.
  2. Simplify Denominator: Simplify the denominator.\newlineThe denominator is k5×k5k^5 \times k^5. We add the exponents because the bases are the same and we are multiplying.\newlinek5×k5=k(5+5)=k10.k^5 \times k^5 = k^{(5 + 5)} = k^{10}.
  3. Divide Powers of kk: Divide the powers of kk. Now we have k3k10\frac{k^3}{k^{10}}. We subtract the exponent in the denominator from the exponent in the numerator because we are dividing. k3k10=k(310)=k7\frac{k^3}{k^{10}} = k^{(3 - 10)} = k^{-7}.
  4. Express Answer: Express the answer with a positive exponent.\newlineSince we cannot have negative exponents in the final answer, we rewrite k7k^{-7} as 1k7\frac{1}{k^7}.

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