Question

express the following fraction in simplest form, only using positive exponents.\\(\frac{4y^{-10}}{-2(y^{-1})^3}\\)

Explanation:

Step1: Simplify coefficient

$\frac{4}{-2} = -2$

Step2: Simplify denominator exponent

$(y^{-1})^3 = y^{-1 \times 3} = y^{-3}$

Step3: Rewrite fraction with simplified terms

$\frac{4y^{-10}}{-2(y^{-1})^3} = \frac{-2y^{-10}}{y^{-3}}$

Step4: Subtract exponents of $y$

$y^{-10 - (-3)} = y^{-7}$

Step5: Convert to positive exponents

$y^{-7} = \frac{1}{y^7}$

Step6: Combine with coefficient

$-2 \times \frac{1}{y^7}$

Answer:

$\frac{-2}{y^7}$