Question - Simplifying a Fraction with Exponents
Solution:
Given the expression $$\frac{4a^6b^5c^{-2}}{(2a^{-4}b^6c)^3}$$, simplify as follows:$$\left(\frac{4a^6b^5c^{-2}}{(2a^{-4}b^6c)^3}\right) = \frac{4a^6b^5c^{-2}}{8a^{-12}b^{18}c^3}$$Apply the exponent rule $$a^m \cdot a^n = a^{m+n}$$ and simplify:$$= 4a^{6 - (-12)}b^{5 - 18}c^{-2 - 3}$$$$= 4a^{18}b^{-13}c^{-5}$$$$= \frac{4a^{18}}{b^{13}c^{5}}$$Thus, the final simplified form is $$\frac{4a^{18}}{b^{13}c^{5}}$$.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com