Problem: 15304515=\dfrac{15^{30}}{45^{15}}=45151530=
Answer Choices:
A. (13)15\left(\dfrac{1}{3}\right)^{15}(31)15
B. (13)2\left(\dfrac{1}{3}\right)^{2}(31)2
C. 111
D. 3153^{15}315
E. 5155^{15}515
Solution:
15304515=330530315315515=330−15−15530−15=30515=515.\dfrac{15^{30}}{45^{15}}=\dfrac{3^{30} 5^{30}}{3^{15} 3^{15} 5^{15}}=3^{30-15-15} 5^{30-15}=3^{0} 5^{15}=5^{15}. 45151530=315315515330530=330−15−15530−15=30515=515.
OR\textbf{OR} OR
15304515=1515(1545)15=1515(13)15=(153)15=515.\dfrac{15^{30}}{45^{15}}=15^{15}\left(\dfrac{15}{45}\right)^{15}=15^{15}\left(\dfrac{1}{3}\right)^{15}=\left(\dfrac{15}{3}\right)^{15}=5^{15}. 45151530=1515(4515)15=1515(31)15=(315)15=515.