Solve: (1/4×6×9)^(-4) Using Negative Exponent Rules

Insert the corresponding expression:

$\left(\frac{1}{4\times6\times9}\right)^{-4}=$

Video Solution

Solution Steps

00:00 Simplify the following problem

00:03 According to the power laws, a fraction that is raised to the power (N)

00:07 equals a fraction where both the numerator and denominator are raised to the power (N)

00:11 We will apply this formula to our exercise

00:15 We will raise both the numerator and denominator to the appropriate power, maintaining the parentheses

00:22 According to the power laws, a product that is raised to the power (N)

00:26 equals the product broken down into factors where each factor is raised to power (N)

00:29 We will apply this formula to our exercise

00:32 We will breakdown each multiplication operation into factors and raise them to the appropriate power (N)

00:37 This is the solution

Step-by-Step Solution

To solve this expression, we need to apply the rules of exponents to simplify $\left(\frac{1}{4 \times 6 \times 9}\right)^{-4}$ .

First, using the power of a fraction rule $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$ , we express each term separately as follows:

$(4 \times 6 \times 9)^{-4} = 4^{-4} \times 6^{-4} \times 9^{-4}$

Therefore, the original negative exponent transforms to a multiplication of three positive exponents in the denominator represented as:

$\frac{1^{-4}}{4^{-4} \times 6^{-4} \times 9^{-4}}$

Thus, the corresponding expression in terms of powers with negative exponents is:

$\frac{1^{-4}}{4^{-4} \times 6^{-4} \times 9^{-4}}$

The correct answer is Choice 4.