Question

Simplify the following expressions. Write your answers as a power. Complete problems 1 through 6.

Answer 1

The expression is given to be:

`(5^4\cdot5^2)/(5^3)`

Recall the multiplication rule of exponent given to be:

`x^a\cdot x^b=x^(a+b)`

Therefore, we can simplify the numerator to be:

`5^4\cdot5^2=5^(4+2)=5^6`

Hence, the expression becomes:

`\Rightarrow(5^6)/(5^3)`

Recall the division rule of exponent given to be:

`(x^a)/(x^b)=x^(a-b)`

Therefore, the expression becomes:

`(5^6)/(5^3)=5^(6-3)=5^3`

Evaluating the answer, we have:

`5^3=125`

Therefore, the answer is:

`(5^4\cdot5^2)/(5^3)=125`