Question

Solve using exponential laws-
(5^3)^2 x (25)^2 divided by 5^7

Answer 1

Hello!

Answer:

`\Large \boxed{\sf 5^3 = 125}`

Explanation:

We have these formulas:

`\sf (x^a)^b = x^{a * b`

`\sf x^a * x^b = x^{a+b`

`\sf x^a / x^b = x^{a-b`

Applicate the formulas:

`\sf (5^(3) )^(2) * (25)^2 / 5^7\\\\= 5^(3 *2) * (5^2)^2 / 5^7\\\\= 5^6 * 5^(2*2) / 5^7\\\\= 5^6 * 5^4 / 5^7\\\\= 5^(6+4) / 5^7\\\\= 5^(10) / 5^7\\\\= 5^(10-7)\\\\\boxed{\sf = 5^3}\\\\\boxed{\sf = 125}`