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nevsk [136]
2 years ago
6

Simplify the following expression (x^0 y^2/3 z^-2)^3/2 divided by (x^2z^1/2)^-6

Mathematics
1 answer:
sergij07 [2.7K]2 years ago
6 0

\dfrac{\left(x^0 y^{\tfrac 23} z^{-2} \right)^{\tfrac 32}}{\left(x^2 z^{\tfrac 12} \right)^{-6}}\\\\\\=\dfrac{1\cdot \left( y^{\tfrac 23}\right)^{\tfrac 32} \cdot \left(z^{-2} \right)^{\tfrac 32}}{\left(x^2 \right)^{-6} \cdot \left( z^{\tfrac 12} \right)^{-6}}~~~~~~~~~~~~~~~~~~;\left[(ab)^m = a^m b^m\right]\\\\\\=\dfrac{y^{1} \cdot z^{-3}}{x^{-12} \cdot z^{-3}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[(a^m)^n = a^{mn}\right]\\\\\\=\dfrac{y}{x^{-12}}\\\\\\

=\dfrac{y}{\tfrac 1{x^{12}}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[a^{-m} = \dfrac 1{a^m} } \right]\\\\\\=yx^{12}

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