Question

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

Answer 1

The expression is given to be:

$\frac{5^4\cdot5^2}{5^3}$

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:

$\Rightarrow\frac{5^6}{5^3}$

Recall the division rule of exponent given to be:

$\frac{x^a}{x^b}=x^{a-b}$

Therefore, the expression becomes:

$\frac{5^6}{5^3}=5^{6-3}=5^3$

Evaluating the answer, we have:

$5^3=125$

Therefore, the answer is:

$\frac{5^4\cdot5^2}{5^3}=125$