Question

Simplify the expression.

[(11 - 4)^3]^2 ÷ (4 + 3)^5

Answer 1

7

Explanation:

`\left[\left(11\:-\:4\right)^3\right]^2\:/ \left(4\:+\:3\right)^5\\\\(\left(\left(11-4\right)^3\right)^2)/(\left(4+3\right)^5)\\\\\mathrm{Subtract\:the\:numbers:}\:11-4=7\\\\=(\left(7^3\right)^2)/(\left(4+3\right)^5)\\\\\mathrm{Add\:the\:numbers:}\:4+3=7\\\\=(\left(7^3\right)^2)/(7^5)\\\\\left(7^3\right)^2=7^6\\\\=(7^6)/(7^5)\\\\\mathrm{Apply\:exponent\:rule}:\quad (x^a)/(x^b)=x^(a-b)\\\\(7^6)/(7^5)=7^(6-5)\\\\\mathrm{Subtract\:the\:numbers:}\:6-5=1\\\\=7`