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

Question

Choose the expression that corresponds to the following:

$\left(5\times8\right)^{-5}=$

00:00 Simplify the following problem

00:03 According to exponent laws, when we have a negative exponent

00:06 Therefore we can convert to the reciprocal number and obtain a positive exponent

00:11 We will apply this formula to our exercise

00:16 We write the reciprocal number (1 divided by the number)

00:19 Proceed to raise to the positive exponent

00:22 This is the 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.

$\frac{1}{\left(5\times8\right)^5}$