Simplify (7×9×6)^-6: Converting Negative Power to Fraction

Insert the corresponding expression:

$\frac{1}{\left(7\times9\times6\right)^{-6}}=$

Video Solution

Solution Steps

00:00 Simplify the following problem

00:03 Apply the exponent laws in order to simplify the negative exponents

00:07 Convert to the reciprocal number and raise to the power multiplied by (-1)

00:10 We'll apply this formula to our exercise

00:14 Convert to the reciprocal number (1 divided by the number)

00:20 Raise to the power multiplied by (-1)

00:24 This is the solution

Step-by-Step Solution

To solve the expression $\frac{1}{\left(7\times9\times6\right)^{-6}}$ , we will employ exponent rules:

Step 1: Recognize that the expression has a negative exponent in the denominator. By the rule of negative exponents, we have $\left(a^n\right)^{-m} = \frac{1}{\left(a^n\right)^m} = \left(a^n\right)^m$ .
Step 2: Therefore, the negative exponent $-6$ becomes positive when moved from the denominator: $\left(7 \times 9 \times 6\right)^{-6}$ becomes $\left(7 \times 9 \times 6\right)^{6}$ once moved to the numerator.

Thus, rewriting the expression, we get $\left(7 \times 9 \times 6\right)^6$ .

The correct multiple-choice answer is choice 3: $\left(7 \times 9 \times 6\right)^6$ .