Question

1) 7^12*5^9/35^10 2)2^6*5^4/10^3 3)6^12/3^10*2^11

Answer 1

Вроде правильно)))))).

Answer 2

Let's simplify the given expressions step by step:

1. $\frac{7^{12} \times 5^9}{35^{10}}$:

First, we can simplify the denominator: $35 = 7 \times 5$ $35^{10} = (7 \times 5)^{10} = 7^{10} \times 5^{10}$

Now we can rewrite the expression: $\frac{7^{12} \times 5^9}{7^{10} \times 5^{10}}$

Using the properties of exponents (subtracting exponents when dividing with the same base), we get: $7^{12 - 10} \times 5^{9 - 10} = 7^2 \times 5^{-1}$

Now, we can calculate the value: $7^2 \times \frac{1}{5} = 49 \times \frac{1}{5} = 9.8$

2. $\frac{2^6 \times 5^4}{10^3}$:

First, we can simplify the denominator: $10 = 2 \times 5$ $10^3 = (2 \times 5)^3 = 2^3 \times 5^3$

Now we can rewrite the expression: $\frac{2^6 \times 5^4}{2^3 \times 5^3}$

Using the properties of exponents (subtracting exponents when dividing with the same base), we get: $2^{6 - 3} \times 5^{4 - 3} = 2^3 \times 5^1$

Now, we can calculate the value: $2^3 \times 5 = 8 \times 5 = 40$

3. $\frac{6^{12}}{3^{10} \times 2^{11}}$:

Using the properties of exponents (subtracting exponents when dividing with the same base), we get: $6^{12} \div 3^{10} \times 2^{-11}$

Now, let's simplify each term separately: $6^{12} = (2 \times 3)^{12} = 2^{12} \times 3^{12}$ $3^{10} = 3^{10} \times 1$ (Anything divided by 1 is itself)

Now, let's rewrite the expression with the simplified terms: $\frac{2^{12} \times 3^{12}}{3^{10} \times 2^{11}}$

Using the properties of exponents (subtracting exponents when dividing with the same base), we get: $2^{12 - 11} \times 3^{12 - 10} = 2 \times 3^2$

Now, we can calculate the value: $2 \times 9 = 18$