Simplify the Fraction: 1/(2⁷ × 9⁷ × 5⁷) Expression

Question

Insert the corresponding expression:

$\frac{1}{2^7\times9^7\times5^7}=$

00:00 Simplify the following problem

00:03 Break down the fraction into 3 smaller fractions

00:12 Apply the exponent laws in order to simplify the negative exponents

00:15 Convert to the reciprocal number and raise to the power of (-1)

00:19 Apply this formula to our exercise

00:29 Raise to the power of (-1)

00:48 Convert to the reciprocal number (1 divided by the number)

01:14 This is the solution

To transform the given expression into one involving negative exponents, we work as follows:

Given expression: $\frac{1}{2^7 \times 9^7 \times 5^7}$

Utilizing the negative exponent rule, $\frac{1}{a^n} = a^{-n}$ , we transform each term in the denominator:

Thus, the expression becomes:

$2^{-7} \times 9^{-7} \times 5^{-7}$

This expression corresponds to applying the negative exponent formula to each factor from the denominator.

Therefore, the solution to the problem is $2^{-7} \times 9^{-7} \times 5^{-7}$ .

$2^{-7}\times9^{-7}\times5^{-7}$