Question

Which expression is equivalent to -3a^-2b^3/15a^-7b^-1

Answer 1

Answer:

$\large\boxed{\dfrac{-3a^{-2}b^3}{15a^{-7}b^{-1}}=-\dfrac{1}{5}a^5b^4=-\dfrac{a^5b^4}{5}}$

Step-by-step explanation:

$\dfrac{-3a^{-2}b^3}{15a^{-7}b^{-1}}=\dfrac{-3}{15}\cdot \dfrac{a^{-2}}{a^{-7}}\cdot\dfrac{b^3}{b^{-1}}\qquad\text{use}\ \dfrac{x^n}{x^m}=x^{n-m}\\\\=-\dfrac{3\!\!\!\!\diagup^1}{15\!\!\!\!\!\diagup_5}\cdot a^{-2-(-7)}\cdot b^{3-(-1)}=-\dfrac{1}{5}a^{-2+7}b^{3+1}=-\dfrac{1}{5}a^5b^4$