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Simplify (-3)3 and x2 z⁻³.

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2 parts
c
-27
d

x2z3\frac{x^2}{z^3}

Step-by-step solution

4 steps

Here are the solutions for the remaining parts:

Part c· 1 step

Simplify (−3)3(-3)^3

  1. Calculate the power.

    (−3)3=(−3)×(−3)×(−3)(-3)^3 = (-3) \times (-3) \times (-3) (−3)×(−3)=9(-3) \times (-3) = 9 9×(−3)=−279 \times (-3) = -27

    The simplified expression is −27\boxed{-27}.

Part d

x2z3\frac{x^2}{z^3}

Simplify x2z−3x^2 z^{-3}

  1. Convert the term with the negative exponent to a positive exponent using the rule a−n=1ana^{-n} = \frac{1}{a^n}.

    z−3=1z3z^{-3} = \frac{1}{z^3}

  2. Substitute this back into the expression.

    x2×1z3x^2 \times \frac{1}{z^3}

  3. Combine the terms.

    x2z3\frac{x^2}{z^3}

    The simplified expression is x2z3\boxed{\frac{x^2}{z^3}}.

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