Questions: Express the following fraction in simplest form, only using positive exponents.
5(t^(-4) x^(-5))^(-1) / (3 t^4 x^(-1))
Transcript text: Express the following fraction in simplest form, only using positive exponents.
\[
\frac{5\left(t^{-4} x^{-5}\right)^{-1}}{3 t^{4} x^{-1}}
\]
Solution
Solution Steps
Step 1: Simplify the numerator
The numerator is 5(t−4x−5)−1. Using the power of a power rule (am)n=am⋅n, we simplify the expression inside the parentheses:
(t−4x−5)−1=t4x5.
Thus, the numerator becomes:
5⋅t4x5.
Step 2: Rewrite the denominator
The denominator is 3t4x−1. Rewrite x−1 as x1:
3t4x−1=3t4⋅x1.
Step 3: Combine the numerator and denominator
Now, divide the numerator by the denominator:
3t4⋅x15t4x5.
Simplify by canceling t4 in the numerator and denominator:
3⋅x15x5.
Multiply by the reciprocal of x1:
35x5⋅x=35x6.