Solve (3/280)^(-2): Negative Exponent with Complex Fraction

Insert the corresponding expression:

$\left(\frac{3}{5\times8\times7}\right)^{-2}=$

Video Solution

Solution Steps

00:00 Simplify the following problem

00:03 According to the laws of exponents, 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)

00:10 We will apply this formula to our exercise

00:15 Raise both the numerator and denominator to the appropriate power, maintaining parentheses

00:20 According to the laws of exponents, a product raised to the power (N)

00:24 is equal to the product broken down into factors where each factor is raised to the power (N)

00:27 We will apply this formula to our exercise

00:30 Break down each multiplication into factors and raise them to the appropriate power (N)

00:37 This is the solution

Step-by-Step Solution

To solve this problem, let's break down the expression $\left(\frac{3}{5 \times 8 \times 7}\right)^{-2}$ :

Step 1: Recognize that we have a fraction raised to a negative exponent.
Step 2: Apply the power of a fraction rule: $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$ .
Step 3: Specifically, apply the rule with a negative exponent: $\left(\frac{3}{5 \times 8 \times 7}\right)^{-2} = \frac{3^{-2}}{(5 \times 8 \times 7)^{-2}}$ .
Step 4: Use the negative exponent rule for each element in the expression $(5 \times 8 \times 7)^{-2} = 5^{-2} \times 8^{-2} \times 7^{-2}$ .

This gives us the expression: $\frac{3^{-2}}{5^{-2} \times 8^{-2} \times 7^{-2}}$ .

Therefore, the correct expression is $\frac{3^{-2}}{5^{-2} \times 8^{-2} \times 7^{-2}}$ .