Simplify the expressions. Remove all negative and zero exponents. Assume all expressions are defined. $\frac { a ^ { 2 } b ^ { - 1 } } { a ^ { - 1 } b ^ { 7 } }$
A) $\frac { b ^ { 3 } } { a ^ { 8 } }$
B) $\frac { a ^ { 2 } } { b ^ { 7 } }$
C) $\frac { b ^ { 8 } } { a ^ { 3 } }$
D) $\frac { b ^ { 2 } } { a ^ { 7 } }$
E) $\frac { a ^ { 3 } } { b ^ { 8 } }$

Question

Quizplus · Accepted Answer

To simplify the expression, use the properties of exponents: $\frac{a^m}{a^n} = a^{m-n}$ and $\frac{b^m}{b^n} = b^{m-n}$. Applying these rules, we get $\frac{a^{2-(-1)}}{b^{(-1)-7}} = \frac{a^{3}}{b^{-8}}$, which simplifies further to $\frac{a^3}{b^8}$ by moving $b^{-8}$ to the denominator as $b^8$.

Simplify the Expressions a2b−1a−1b7\frac { a ^ { 2 } b ^ { - 1 } } { a ^ { - 1 } b ^ { 7 } }a−1b7a2b−1​

Simplify the Expressions $\frac { a ^ { 2 } b ^ { - 1 } } { a ^ { - 1 } b ^ { 7 } }$