Question

25^3 * 125^2 / 5^10 = ???

Answer 1

Ответ: 25

Пошаговое объяснение:

Answer 2

Let's break down the expression step by step:

1. $25^3$ means $25$ raised to the power of $3$, which is $25 \times 25 \times 25$.
2. $125^2$ means $125$ raised to the power of $2$, which is $125 \times 125$.
3. $5^{10}$ means $5$ raised to the power of $10$, which is $5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5$.

Now, let's substitute these values back into the expression:

$\frac{25^3 \times 125^2}{5^{10}} = \frac{25 \times 25 \times 25 \times 125 \times 125}{5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5}$

Now, cancel out common factors in the numerator and denominator:

$\frac{5^3 \times 25^2 \times 5^3 \times 5^3}{5^{10}} = \frac{5^9 \times 25^2}{5^{10}}$

Since $25^2 = 5^4$, we can simplify further:

$\frac{5^9 \times 5^4}{5^{10}} = \frac{5^{13}}{5^{10}}$

Using the rule $a^m / a^n = a^{m-n}$:

$5^{13 - 10} = 5^3 = 125$

So, $25^3 \times 125^2 / 5^10$ equals $125$.