Simplify 1/(4×5×6)^6: Complex Fraction with Product Exponent

Question

Insert the corresponding expression:

$\frac{1}{\left(4\times5\times6\right)^6}=$

00:00 Simplify the following problem

00:14 A negative x negative always equals a positive

00:20 Apply the exponent laws in order to simplify the negative exponents

00:24 Convert to the reciprocal number and raise to the power (-1)

00:29 Apply this formula to our exercise

00:33 Convert to the reciprocal number (1 divided by the number)

00:37 Raise to power (-1)

00:41 This is the solution

To solve this problem, we will express the given fraction using the rules of exponents:

Given expression:

Applying the rule for negative exponents, $\frac{1}{a^n} = a^{-n}$ , we can rewrite the expression as follows:

Step 1: Recognize that the expression inside the fraction's denominator is $\left(4\times5\times6\right)^6$ .

Step 2: Apply the negative exponent rule:

\frac{1}{\left(4\times5\times6\right)^6} = \left(4\times5\times6\right)^{-6}

Therefore, the equivalent expression is

$\left(4\times5\times6\right)^{-6}$ .

$\left(4\times5\times6\right)^{-6}$