Simplify (3x)^8/(3x): Power and Division Expression

$\frac{\left(3\times x\right)^8}{\left(3\times x\right)}$

Let's solve the expression $\frac{(3 \times x)^8}{(3 \times x)}$ step by step using the Power of a Quotient Rule for Exponents.

The expression given is:

$\frac{(3 \times x)^8}{(3 \times x)}$

The Power of a Quotient Rule states that for any non-zero number $a$, and integers $m$ and $n$, the expression $\frac{a^m}{a^n}$ is equal to $a^{m-n}$.

In this problem, $a$ is $3 \times x$, $m = 8$, and $n = 1$.

Applying the Power of a Quotient Rule:

• Subtract the exponent in the denominator from the exponent in the numerator. So we have $(3 \times x)^{8-1}$.

Thus, the simplified form of the expression is:

$(3 \times x)^{7}$

The solution to the question is: $(3 \times x)^{7}$.