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Alona [7]
3 years ago
12

Simplify the expression

Mathematics
1 answer:
alekssr [168]3 years ago
8 0

(2.5a^{8n})^3 . (0.4^{7n})^3 = 15.625 \times a^{24n} \times (0.4^{21})^n

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

We have to simplify the given expression

<em><u>Given expression is:</u></em>

(2.5a^{8n})^3 . (0.4^{7n})^3

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

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

<em><u>Thus the given expression becomes,</u></em>

(2.5a^{8n})^3 . (0.4^{7n})^3 = (2.5)^3(a)^{8n \times 3} \times (0.4)^{7n \times 3}

<em><u>Simplify the exponents</u></em>

(2.5a^{8n})^3 . (0.4^{7n})^3 = 15.625 \times a^{24n} \times 0.4^{21n}

Again use the law of exponent for 0.4^{21n}

0.4^{21n} = (0.4^{21})^n

<em><u>Substitute in above expression</u></em>

(2.5a^{8n})^3 . (0.4^{7n})^3 = 15.625 \times a^{24n} \times (0.4^{21})^n

Thus the given expression is simplified

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