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Simplify. Express your answer using positive exponents. (w^(-3))/(w^(-3))

Simplify. Express your answer using positive exponents.\newlinew−3w−3\frac{w^{-3}} {w^{-3}}

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Full solution

Q. Simplify. Express your answer using positive exponents.\newlinew−3w−3\frac{w^{-3}} {w^{-3}}
  1. Identify operation for exponents: Identify the operation needed for the exponents −3-3 and −3-3. When we divide powers with the same base, we subtract the exponents.
  2. Simplify expression: Simplify the expression (w−3)/(w−3)(w^{-3})/(w^{-3}). We apply the rule for dividing powers with the same base: wa/wb=wa−bw^a / w^b = w^{a-b}. So, (w−3)/(w−3)=w−3−(−3)=w0(w^{-3})/(w^{-3}) = w^{-3 - (-3)} = w^{0}.
  3. Apply rule for dividing powers: Recall that any non-zero number raised to the power of 00 is 11. Therefore, w0=1w^{0} = 1.

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