Solve (1/5×6×7)^(-3): Negative Exponent with Sequential Products

Question

Insert the corresponding expression:

$\left(\frac{1}{5\times6\times7}\right)^{-3}=$

00:00 Simplify the following problem

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

00:08 equals the reciprocal fraction raised to the opposite 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

00:23 This is the solution

To solve the expression $\left(\frac{1}{5\times6\times7}\right)^{-3}$ , follow these steps:

Step 1: Recognize that the expression $\left(\frac{1}{5\times6\times7}\right)^{-3}$ has a negative exponent.
Step 2: Use the rule for negative exponents: $\left(\frac{1}{a}\right)^{-n} = a^{n}$ .
Step 3: Apply the rule: $\left(\frac{1}{5\times6\times7}\right)^{-3} = \left(5\times6\times7\right)^{3}$ .

Therefore, the expression simplifies to $\left(5\times6\times7\right)^3$ .

The correct answer is $\left(5\times6\times7\right)^3$ .

$\left(5\times6\times7\right)^3$