[tex](2.5a^{8n})^3 . (0.4^{7n})^3 = 15.625 \times a^{24n} \times (0.4^{21})^n[/tex]
Solution:
We have to simplify the given expression
Given expression is:
[tex](2.5a^{8n})^3 . (0.4^{7n})^3[/tex]
Use the law of exponent
[tex](a^m)^n = a^{mn}[/tex]
Thus the given expression becomes,
[tex](2.5a^{8n})^3 . (0.4^{7n})^3 = (2.5)^3(a)^{8n \times 3} \times (0.4)^{7n \times 3}[/tex]
Simplify the exponents
[tex](2.5a^{8n})^3 . (0.4^{7n})^3 = 15.625 \times a^{24n} \times 0.4^{21n}[/tex]
Again use the law of exponent for [tex]0.4^{21n}[/tex]
[tex]0.4^{21n} = (0.4^{21})^n[/tex]
Substitute in above expression
[tex](2.5a^{8n})^3 . (0.4^{7n})^3 = 15.625 \times a^{24n} \times (0.4^{21})^n[/tex]
Thus the given expression is simplified
