Question

3^-6×9^-2/27^-4 вычислите

Answer 1

3^-6×9^-2/27^-4
3^-6* (3^2)^-2 / (3^3)^-4
3^-6 * 3^-4 / 3^-12
3^-6*3^8
3^2 = 9

Answer 2

To simplify the expression, let's start by applying the rules of exponents:

1. When you have a negative exponent, you can move the term to the denominator and change the sign of the exponent to make it positive.
2. When you have a fraction with the same base in the numerator and denominator, you can cancel them out.

Let's apply these rules step by step:

1. $3^{-6} = \frac{1}{3^6}$ (Move the term with the negative exponent to the denominator and make the exponent positive.)

2. $9^{-2} = \frac{1}{9^2}$ (Same as above.)

3. $27^{-4} = \frac{1}{27^4}$ (Same as above.)

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

$\frac{3^{-6} \times 9^{-2}}{27^{-4}} = \frac{\frac{1}{3^6} \times \frac{1}{9^2}}{\frac{1}{27^4}}$

Next, simplify the fractions:

$\frac{1}{3^6} = \frac{1}{729}$ (3 raised to the power of 6 is 729.)

$\frac{1}{9^2} = \frac{1}{81}$ (9 raised to the power of 2 is 81.)

$\frac{1}{27^4} = \frac{1}{531441}$ (27 raised to the power of 4 is 531441.)

Substitute these simplified values back into the expression:

$\frac{\frac{1}{3^6} \times \frac{1}{9^2}}{\frac{1}{27^4}} = \frac{\frac{1}{729} \times \frac{1}{81}}{\frac{1}{531441}}$

Now, multiply the fractions:

$\frac{1}{729} \times \frac{1}{81} = \frac{1}{59241}$

Finally, divide by $\frac{1}{531441}$:

$\frac{1}{59241} \div \frac{1}{531441} = \frac{1}{59241} \times 531441 = \frac{531441}{59241}$

Now, let's simplify the fraction:

$\frac{531441}{59241} = 9$

So, $3^{-6} \times 9^{-2} \div 27^{-4} = 9$.