Question

\frac{\left(5^6\right)^2\cdot 3^{14}}{15^{13}}

Answer 1

$\frac{\left(5^6\right)^2\cdot 3^{14}}{15^{13}}=\frac{5^{12} \cdot 3^{12}\cdot 3^{2}}{15^{12}\cdot 5}= \frac{15^{12} \cdot 9}{15^{12}\cdot 5}= 1,8$

Answer 2

To simplify the expression $\frac{\left(5^6\right)^2\cdot 3^{14}}{15^{13}}$, we can use the properties of exponents. Remember that when you raise an exponent to another exponent, you multiply the exponents. Also, $a^m \cdot a^n = a^{m+n}$ and $\frac{a^m}{a^n} = a^{m-n}$.

Let's break down the expression step by step:

1. $(5^6)^2$ means $5^6$ raised to the power of 2, so $(5^6)^2 = 5^{6 \times 2} = 5^{12}$.

2. Now the expression becomes $\frac{5^{12} \cdot 3^{14}}{15^{13}}$.

3. We know that $15 = 5 \times 3$. So, $15^{13} = (5 \times 3)^{13} = 5^{13} \cdot 3^{13}$.

4. Now the expression becomes $\frac{5^{12} \cdot 3^{14}}{5^{13} \cdot 3^{13}}$.

5. Applying the property $\frac{a^m}{a^n} = a^{m-n}$, we can rewrite the expression as $5^{12-13} \cdot 3^{14-13}$.

6. Simplifying further, we get $5^{-1} \cdot 3^1$.

7. $5^{-1}$ means the reciprocal of $5^1$, so $5^{-1} = \frac{1}{5}$.

Now the expression becomes $\frac{1}{5} \cdot 3^1$.

8. Finally, $\frac{1}{5} \cdot 3^1 = \frac{3}{5}$.

So, the simplified value of the expression is $\frac{3}{5}$.