Question

Simplify the expression

Answer 1

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

Solution:

We have to simplify the given expression

Given expression is:

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

Use the law of exponent

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

Thus the given expression becomes,

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

Simplify the exponents

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

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

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

Substitute in above expression

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

Thus the given expression is simplified