Simplify (2×7)⁴ ÷ (2×7)⁷: Exponent Division Practice

Let's solve the given expression by applying the rules of exponents. The expression given is:
$\frac{\left(2\times7\right)^4}{\left(2\times7\right)^7}$

We know the rule for dividing powers with the same base: $\frac{a^m}{a^n} = a^{m-n}$.
In this case, the base is $2 \times 7$, and we have the exponent 4 in the numerator and 7 in the denominator.

Applying the rule, we subtract the exponent in the denominator from the exponent in the numerator:

• $\frac{\left(2\times7\right)^4}{\left(2\times7\right)^7} = \left(2\times7\right)^{4-7}$.

Now simplify the exponent:

• $4 - 7 = -3$

Thus, the expression becomes:
$\left(2\times7\right)^{-3}$.

The solution to the question is: $\left(2\times7\right)^{-3}$.