Evaluate (7×11×19)/(3×12×15) Raised to Power -6

Insert the corresponding expression:

$\left(\frac{7\times11\times19}{3\times12\times15}\right)^{-6}=$

Video Solution

Solution Steps

00:00 Simplify the following problem

00:03 According to the laws of exponents, a fraction raised to a negative power (-N)

00:07 is equal to the reciprocal fraction raised to the positive power (N)

00:11 We will apply this formula to our exercise

00:15 We will convert to the reciprocal number and raise it to the opposite power

00:26 This is the solution

Step-by-Step Solution

To solve this problem, we'll apply the rules for negative exponents:

We start with the expression: $\left(\frac{7 \times 11 \times 19}{3 \times 12 \times 15}\right)^{-6}$ .

By the rule for negative exponents, $(a/b)^{-n} = (b/a)^n$ , we invert the fraction and change the exponent from $-6$ to $6$ :

$\left(\frac{3 \times 12 \times 15}{7 \times 11 \times 19}\right)^6$

This transformation capitalizes on the idea that negative exponents reflect a reciprocal relationship.

Therefore, the expression with positive exponents is: $\left(\frac{3 \times 12 \times 15}{7 \times 11 \times 19}\right)^6$ .