First we must convert these to the same bases. We can rewrite 45^15 as 15^15 3^15 Now 15^3015^15 3^15 Canceling.... 15^153^15 (153)^15 5^15 5^15

Browse · harp

smc

prealgebra intermediate

Problem

\frac{1 5 ^{30}}{4 5 ^{15}} =

(A)

(1/3)^{1} 5

(B)

(1/3)^{2}

(C)

1

(D)

3^{1} 5

(E)

5^{15}

Solution

First we must convert these to the same bases. We can rewrite

4 5^{15}

1 5^{15} \cdot 3^{15}

Now

\frac{1 5 ^{30}}{1 5 ^{15} \cdot 3 ^{15}}

Canceling....

\frac{1 5 ^{15}}{3 ^{15}} \Rightarrow (\frac{15}{3})^{15} \Rightarrow 5^{15}

5^{15}

Final answer