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Simplify. Express your answer using positive exponents. \newline2z2(2z9)(z6)\frac{2z^2}{(2z^9)(z^6)}

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Full solution

Q. Simplify. Express your answer using positive exponents. \newline2z2(2z9)(z6)\frac{2z^2}{(2z^9)(z^6)}
  1. Rewrite and Combine Terms: First, rewrite the expression to make it easier to handle. Combine the terms in the denominator. \newline2z22z9⋅z6\frac{2z^2}{2z^9 \cdot z^6}
  2. Multiply Exponents: Next, multiply the exponents in the denominator. When multiplying with the same base, add the exponents.\newline2z9×z6=2z9+6=2z152z^9 \times z^6 = 2z^{9+6} = 2z^{15}
  3. Simplify by Dividing: Now, simplify the expression by dividing the terms. When dividing powers with the same base, subtract the exponents. \newline2z22z15=(22)⋅z(2−15)=z−13\frac{2z^2}{2z^{15}} = \left(\frac{2}{2}\right) \cdot z^{(2-15)} = z^{-13}
  4. Rewrite Negative Exponent: Since the problem asks for positive exponents, rewrite the negative exponent as a positive exponent in the denominator.\newlinez−13=1z13z^{-13} = \frac{1}{z^{13}}

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