Math Problem Statement

Jawablah pertanyaan berikut

Diketahui x = -2, y = 2, dan z = 3 maka hasil dari (xy^3)^2 (yz^{-1}/z^2)^{-3} adalah...

Solution

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11. Diketahui x=2x = -2, y=2y = 2, dan z=3z = 3, maka hasil dari (xy3)2(yz1z2)3(xy^3)^2 \cdot \left( \frac{yz^{-1}}{z^2} \right)^{-3} adalah:

Solution:

  1. (xy3)2=(223)2=(28)2=(16)2=256(xy^3)^2 = (-2 \cdot 2^3)^2 = (-2 \cdot 8)^2 = (-16)^2 = 256.
  2. Simplify yz1z2=23132=2139=227\frac{yz^{-1}}{z^2} = \frac{2 \cdot 3^{-1}}{3^2} = \frac{2 \cdot \frac{1}{3}}{9} = \frac{2}{27}.
  3. Raise it to the power of 3-3: (227)3=27323=196838\left( \frac{2}{27} \right)^{-3} = \frac{27^3}{2^3} = \frac{19683}{8}.
  4. Multiply 256196838=256196838=629856÷8=78732256 \cdot \frac{19683}{8} = \frac{256 \cdot 19683}{8} = 629856 \div 8 = 78732.
  5. Answer: 7873278732.

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponentiation
Simplification of expressions

Formulas

(a^m)^n = a^{m * n}
Simplifying fractional powers
Negative exponent rules

Theorems

Laws of exponents
Fraction simplification

Suitable Grade Level

Grades 8-10