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Zepler [3.9K]
3 years ago
14

Write (8a-^3) -2/3 in simplest form

Mathematics
1 answer:
Anna71 [15]3 years ago
8 0

(8a^{-3})^{\frac{-2}{3}} = \frac{a^2}{4}

<em><u>Solution:</u></em>

<em><u>Given that,</u></em>

(8a^{-3})^{\frac{-2}{3}

We have to write in simplest form

<em><u>Use the following law of exponent</u></em>

(a^m)^n = a^{mn}

Using this, simplify the given expression

(8a^{-3})^{\frac{-2}{3}} = 8^{\frac{-2}{3}} \times a^{ -3 \times \frac{-2}{3}}\\\\Simplifying\ we\ get\\\\(8a^{-3})^{\frac{-2}{3}} = 8^{\frac{-2}{3}} \times a^2\\\\We\ know\ that\ 8 = 2^3\\\\Therefore\\\\(8a^{-3})^{\frac{-2}{3}} =2^3^{\frac{-2}{3}} \times a^2\\\\(8a^{-3})^{\frac{-2}{3}} =2^{-2} \times a^2\\\\(8a^{-3})^{\frac{-2}{3}} = \frac{a^2}{4}

Thus the given expression is simplified

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