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

00:13 Let's make this math problem simpler.

00:17 When a fraction is raised to a negative power, like negative N,

00:21 it's the same as the reciprocal of that fraction raised to positive N.

00:25 We'll use this idea in our exercise.

00:28 First, find the reciprocal, then use the opposite power.

00:39 And that's how we find 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: $\left(\frac{3 \times 12 \times 15}{7 \times 11 \times 19}\right)^6$ .