Question

Evaluate the value of the following:

$\frac{3^5\times 5^5}{{\left(15\right)}^3}$

Answer 1

Hint: As we know the following laws of exponents is:

1. $x^a\times x^b=x^{a+b}$
2. ${(x\times y)}^a=x^a\times y^a$
3. $\frac{x^a}{x^b}=x^{a-b}$

Step 1: Given number: $\frac{3^5\times 5^5}{{\left(15\right)}^3}$

Step2: Evaluate given term.

Using the above law of exponents:

$$\begin{gathered} \frac{3^5\times 5^5}{{\left(15\right)}^3}=\frac{3^5\times 5^5}{{(5\times 3)}^3} \\ =\frac{3^5\times 5^5}{5^3\times 3^3}\left\{U\sin g{(x\times y)}^a=x^a\times y^a\right\} \\ =3^{5-3}\times 5^{5-3}\left\{U\sin g\frac{x^a}{x^b}=x^{a-b}\right\} \\ =3^2\times 5^2 \\ =9\times 25=225 \end{gathered}$$

Hence $225$ is the required value.