Evaluate (5×8)^(-5): Negative Exponent Expression Solution

To solve the expression $\left(5\times8\right)^{-5}$, we need to apply the rules of exponents related to negative exponents.

First, let's recall the rule for negative exponents: for any non-zero number $a$,$a^{-n} = \frac{1}{a^n}$.

Applying this rule to our expression$\left(5\times8\right)^{-5}$:

• The base $5\times8$ is a product of two numbers 5 and 8.

• The exponent is -5, which means we have a negative exponent.

• According to the property of negative exponents, we invert the base and change the sign of the exponent:

Thus, $\left(5\times8\right)^{-5} = \frac{1}{\left(5\times8\right)^5}$.

After applying the rule, we arrive at the expression $\frac{1}{(5 \times 8)^5}$ which matches the given solution.