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horsena [70]
2 years ago
7

Explain me PLEASEEEE!!!

Mathematics
1 answer:
kirza4 [7]2 years ago
8 0

Answer:

\frac{(a^{2})^{3}.a^{-3}}{a^{10}}=\frac{a^{6}.a^{-3}}{a^{10}}=\frac{a^{3}}{a^{10}}=a^{-7}=\frac{1}{a^{7}}

Step-by-step explanation:

Let us revise the properties of exponents

  • a^{m}.a^{n}=a^{m+n}
  • \frac{a^{m}}{a^{n}}=a^{m-n}
  • (a^{m})^{n}=a^{m.n}
  • a^{-m}=\frac{1}{a^{m} }

Let us use these properties to solve the question

→ By using the 3rd property above

∵ (a^{2})^{3}=a^{2.3}=a^{6}

∴ \frac{(a^{2})^{3}.a^{-3}}{a^{10}}=\frac{a^{6}.a^{-3}}{a^{10} }

→ By using the 1st property above

∵ a^{6}.a^{-3}=a^{6+-3}=a^{6-3}=a^{3}

∴  \frac{(a^{2})^{3}.a^{-3}}{a^{10}}=\frac{a^{6}.a^{-3}}{a^{10}}=\frac{a^{3}}{a^{10}}

→ By using the 2nd property above

∵ \frac{a^{3}}{a^{10}}=a^{3-10}=a^{-7}

∴  \frac{(a^{2})^{3}.a^{-3}}{a^{10}}=\frac{a^{6}.a^{-3}}{a^{10}}=\frac{a^{3}}{a^{10}}=a^{-7}

→ By using the 4th property above

∵ a^{-7}=\frac{1}{a^{7}}

∴  \frac{(a^{2})^{3}.a^{-3}}{a^{10}}=\frac{a^{6}.a^{-3}}{a^{10}}=\frac{a^{3}}{a^{10}}=a^{-7}=\frac{1}{a^{7}}

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