Express the following as a single fraction involving positive exponents only. $$4 x ^ { - 3 } - 5 x ^ { - 7 }$$
A) $- \frac { 1 } { x ^ { 10 } }$
B) $4 x ^ { 7 } - 5 x ^ { 3 }$
C) $\frac { 4 x ^ { 4 } - 5 } { x ^ { 7 } }$
D) $\frac { 4 x ^ { 4 } - 5 } { x ^ { 6 } }$
E) $\frac { 1 } { 4 x ^ { 7 } - 5 x ^ { 3 } }$

Question

Quizplus · Accepted Answer

To express the given expression as a single fraction with positive exponents, we find a common denominator, which is $x^7$ (the least common multiple of $x^3$ and $x^7$). We rewrite each term with $x^7$ as the denominator: $4x^{-3} = \frac{4}{x^3}$ becomes $\frac{4x^4}{x^7}$ and $-5x^{-7} = \frac{-5}{x^7}$ remains unchanged. Combining these gives $\frac{4x^4 - 5}{x^7}$.

Express the Following as a Single Fraction Involving Positive Exponents 4x−3−5x−74 x ^ { - 3 } - 5 x ^ { - 7 }4x−3−5x−7

Express the Following as a Single Fraction Involving Positive Exponents $4 x ^ { - 3 } - 5 x ^ { - 7 }$