Simplify 1/(8⁻⁷ × 9⁻⁷ × 5⁻⁷): Negative Exponent Practice

Insert the corresponding expression:

$\frac{1}{8^{-7}\times9^{-7}\times5^{-7}}=$

Video Solution

Solution Steps

00:00 Simplify the following problem

00:03 A product where each factor is raised to the same power (N)

00:08 Can be converted to parentheses of the entire product raised to the power of the factor (N)

00:14 We will apply this formula to our exercise

00:25 Apply the exponent laws in order to simplify the negative exponents

00:29 Convert to the reciprocal number and raise to the power multiplied by (-1)

00:32 We will apply this formula to our exercise

00:35 Convert to the reciprocal number (1 divided by the number)

00:41 Raise to the power multiplied by (-1)

00:44 This is the solution

Step-by-Step Solution

To solve the problem, follow these steps:

Given the expression $\frac{1}{8^{-7} \times 9^{-7} \times 5^{-7}}$ .
Apply the negative exponent rule: Each term in the denominator is raised to a negative power.
Write each term with positive exponents using the reciprocal rule: $\frac{1}{a^{-n}} = a^n$ .
This results in the expression: $8^7 \times 9^7 \times 5^7$ .
The power of a product rule tells us that this is equivalent to $(8 \times 9 \times 5)^7$ .

Therefore, the solution is $\left(8 \times 9 \times 5\right)^7$ .

Comparing with the multiple-choice options provided, the correct choice is: $\left(8 \times 9 \times 5\right)^7$ .