Question

Express your answer using positive exponents:

(tu⁹v⁻¹w⁻⁴)/(t⁻⁶u⁻⁴v⁻¹w⁻¹ * t⁰u⁻¹v⁻³w * t³u⁻¹v⁻¹w)

Answer 1

To express the given complex fraction using positive exponents, simplify the denominator by combining like terms with their exponents and then divide by subtracting exponents with the same base. The final expression is: t^4u^15v^4w^3.

Step-by-step explanation:

To express (tu9v−1w−4)/(t−6u−4v−1w−1 * t0u−1v−3w * t3u−1v−1w) using positive exponents, we need to first simplify the expression inside the parentheses on the denominator. Note that any term raised to the 0 power is 1, and that multiplication of exponents with the same base results in adding the exponents.

Let's break down the denominator into its constituent parts and then combine:

• t−6 * t0 * t3 = t(−6 + 0 + 3) = t−3
• u−4 * u−1 * u−1 = u(−4 + −1 + −1) = u−6
• v−1 * v−3 * v−1 = v(−1 + −3 + −1) = v−5
• w−1 * w = w−1

Now that we've simplified the denominator, the whole expression becomes:

(tu9v−1w−4)/(t−3u−6v−5w−1)

To divide exponents with the same base, we subtract the exponents. Thus:

• tuv−1w−4 / t−3 = t(1 + 3)
• u9/u−6 = u(9 + 6)
• v−1/v−5 = v(−1 - (−5))
• w−4/w−1 = w(−4 - (−1))

The final expression with positive exponents is:

t4u15v4w3