Express the following fraction in simplest form, only using positive exponents.

Question

start fraction, 10, j, to the power minus 3 , divided by, minus, 2, left parenthesis, j, to the power minus 3 , right parenthesis, cubed, end fraction
−2(j
−3
)
3

10j
−3

​

Answer 1

To simplify the expression \(\frac{10 j^{-3}}{-2 (j^{-3})^3}\), we will follow these steps:

1. Simplify the denominator: \[ -2 (j^{-3})^3 = -2 j^{-9} \] This is because when you raise a power to another power, you multiply the exponents: \((-3) \cdot 3 = -9\).

2. Rewrite the fraction: So, we rewrite the fraction: \[ \frac{10 j^{-3}}{-2 j^{-9}} \]

3. Divide the numerical coefficients: The numerical part is: \[ \frac{10}{-2} = -5 \]

4. Divide the variable parts (using the property \(\frac{a^m}{a^n} = a^{m-n}\)): For the variable part, we have: \[ \frac{j^{-3}}{j^{-9}} = j^{-3 - (-9)} = j^{-3 + 9} = j^{6} \]

5. Combine the results: Therefore, the expression simplifies to: \[ -5 j^{6} \]

6. Express in positive exponents: Since the original expression does not have any negative base after simplification, we keep it as is.

So, the final result in simplest form using only positive exponents is: \[ -5 j^{6} \]