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Simplify. Rewrite the expression in the form z^(n). (z^(7))/(z^(-14))=

Simplify.\newlineRewrite the expression in the form \newlineznz^{n}.\newlinez7z−14\frac{z^{7}}{z^{-14}}=

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Full solution

Q. Simplify.\newlineRewrite the expression in the form \newlineznz^{n}.\newlinez7z−14\frac{z^{7}}{z^{-14}}=
  1. Identify base and exponents: Identify the base and the exponents of both the numerator and the denominator. In the numerator, zz is the base raised to the exponent 77. In the denominator, zz is the base raised to the exponent −14-14.
    Base: zz
    Exponent of numerator: 77
    Exponent of denominator: −14-14
  2. Apply quotient rule for exponents: Apply the quotient rule for exponents, which states that when dividing like bases, you subtract the exponent of the denominator from the exponent of the numerator.\newlinez7z−14=z7−(−14)\frac{z^{7}}{z^{-14}} = z^{7 - (-14)}
  3. Perform subtraction in exponent: Perform the subtraction in the exponent.\newlinez(7−(−14))=z(7+14)=z21z^{(7 - (-14))} = z^{(7 + 14)} = z^{21}
  4. Write final simplified expression: Write the final simplified expression.\newlineThe expression z7z−14\frac{z^{7}}{z^{-14}} simplifies to z21z^{21}.

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