Question

80^7/5^8*2^29+5^6*3^6/15^6​

Answer 1

80⁷/(5⁸*2²⁹) + 5⁶*3⁶/15⁶=

(5*8*2)⁷/(5⁸*2²⁹) + (5*3/15)⁶=

5⁷*(2⁴)⁷/(5⁸*2²⁹) + 1⁶=

2²⁸/(5*2²⁹) + 1=

1/(5*2) + 1=1,1  -  это ответ.

Answer 2

Let's break down the expression step by step:

1. $80^{7}$ can be expressed as $2^{7} \cdot 10^{7}$, where $2^{7} = 128$ and $10^{7} = 10,000,000$.

2. $5^{8}$ is $5^{2} \cdot 5^{2} \cdot 5^{2} \cdot 5^{2} = 25 \cdot 25 \cdot 25 \cdot 25 = 625 \cdot 625 = 390,625$.

3. $2^{29}$ is a large number, but we don't need to calculate it exactly for this problem.

4. $5^{6} = 15^{6}$ because $5$ and $15$ share a common factor of $5$, so they both can be expressed as $5^{6}$.

Now, let's rewrite the expression:

$\frac{80^{7}}{5^{8} \cdot 2^{29}} + \frac{5^{6} \cdot 3^{6}}{15^{6}}$

Substitute the values we found earlier:

$\frac{(2^{7} \cdot 10^{7})}{(625 \cdot 2^{29})} + \frac{(5^{6} \cdot 3^{6})}{(5^{6})}$

Now, we can simplify the fractions:

$\frac{2^{7} \cdot 10^{7}}{625 \cdot 2^{29}} + \frac{5^{6} \cdot 3^{6}}{5^{6}}$

Next, simplify further by canceling out common factors:

$\frac{2^{7} \cdot 10^{7}}{625 \cdot 2^{29}} + 3^{6}$

Now, we can calculate the values:

1. $2^{7} = 128$
2. $10^{7} = 10,000,000$
3. $625$ remains the same.
4. $2^{29}$ is a large number, and we'll leave it as is.
5. $3^{6} = 729$

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

$\frac{128 \cdot 10,000,000}{625 \cdot 2^{29}} + 729$

At this point, you can calculate the exact value if you have a calculator, or you can approximate it:

The fraction $\frac{128 \cdot 10,000,000}{625 \cdot 2^{29}}$ is approximately $58.72$ (rounded to two decimal places).

So, the final result is approximately:

$58.72 + 729 = 787.72$ (rounded to two decimal places).

So, $80^{7}/5^{8} \cdot 2^{29} + 5^{6} \cdot 3^{6}/15^{6}$ is approximately equal to $787.72$.