Evaluate (6×5)^(-3): Negative Exponent Expression Problem

Insert the corresponding expression:

$\left(6\times5\right)^{-3}=$

Video Solution

Solution Steps

00:00 Simplify the following problem

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

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

00:10 We'll apply this formula to our exercise

00:13 We'll write the reciprocal number (1 divided by the number)

00:17 Raise to the positive exponent

00:23 In order to open parentheses of an exponent over a product

00:27 Raise each factor to the power

00:30 We'll apply this formula to our exercise

00:37 This is the solution

Step-by-Step Solution

To solve the problem of simplifying $(6 \times 5)^{-3}$ , we will proceed as follows:

Step 1: Apply the power of a product rule, which states $(a \times b)^n = a^n \times b^n$ . In our case, apply this to get $(6 \times 5)^{-3} = 6^{-3} \times 5^{-3}$ .
Step 2: Use the negative exponent rule, which is $a^{-n} = \frac{1}{a^n}$ . Applying this to each term, we find:

Step 3: Multiply the results from Step 2:
$6^{-3} \times 5^{-3} = \left(\frac{1}{6^3}\right) \times \left(\frac{1}{5^3}\right) = \frac{1}{6^3 \times 5^3}$ .

Therefore, the expression $(6 \times 5)^{-3}$ simplifies to $\frac{1}{6^3 \times 5^3}$ .

The correct answer choice is:

$\frac{1}{6^3\times5^3}$