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Simplify the expression, leave your answer in exponential form :Can you show the steps!??
4 months ago
Q:
Simplify the expression, leave your answer in exponential form :Can you show the steps!??
Accepted Solution
A:
[tex]\bf ~~~~~~~~~~~~\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} \qquad \qquad \cfrac{1}{a^n}\implies a^{-n} \qquad \qquad a^n\implies \cfrac{1}{a^{-n}} \\\\ -------------------------------\\\\ \left( \cfrac{16y^0z^{-8}}{x^{\frac{1}{2}}} \right)^{-\frac{3}{4}}\implies \left( \cfrac{x^{\frac{1}{2}}}{16y^0z^{-8}} \right)^{\frac{3}{4}}\implies \left( \cfrac{x^{\frac{1}{2}}}{16(1)z^{-8}} \right)^{\frac{3}{4}}[/tex]
[tex]\bf \left( \cfrac{x^{\frac{1}{2}}}{16z^{-8}} \right)^{\frac{3}{4}}\implies \left( \cfrac{x^{\frac{1}{2}\cdot \frac{3}{4}}}{16^{\frac{3}{4}}z^{-8\cdot \frac{3}{4}}} \right)\implies \left( \cfrac{x^{\frac{3}{8}}}{(2^4)^{\frac{3}{4}}z^{-6}} \right) \\\\\\ \left( \cfrac{x^{\frac{3}{8}}}{2^{4\cdot \frac{3}{4}}z^{-6}} \right)\implies \left( \cfrac{x^{\frac{3}{8}}}{2^3z^{-6}} \right)\implies \cfrac{x^{\frac{3}{8}}z^6}{8}[/tex]