Question

5^-4•5^2. 12^-3:12^-4. (3^-1)^-3. решите

Answer 1

$5^{-4} * 5^{2} = 5^{-4+2} = 5^{-2}= \frac{1}{ 5^{2} } = \frac{1}{25} =0,04$

$12^{-3}: 12^{-4} = 12^{-3-(-4)} = 12^{-3+4} =12$

$( 3^{-1}) ^{-3}= 3^{-1*(-3)} = 3^{3}=27$

Answer 2

To solve the given expression, let's simplify each part step by step:

1. Simplify 5^-4 • 5^2: Remember the rule: a^m • a^n = a^(m+n) So, 5^-4 • 5^2 = 5^(2-4) = 5^-2 = 1/5^2 = 1/25.

2. Simplify 12^-3 : 12^-4: Remember the rule: a^m / a^n = a^(m-n) So, 12^-3 : 12^-4 = 12^(-3-(-4)) = 12^-3+4 = 12^1 = 12.

3. Simplify (3^-1)^-3: Remember the rule: (a^m)^n = a^(mn) So, (3^-1)^-3 = 3^(-1-3) = 3^3 = 27.

Now, let's combine the simplified expressions:

1. 5^-4 • 5^2 = 1/25
2. 12^-3 : 12^-4 = 12
3. (3^-1)^-3 = 27

Now, multiply all the simplified expressions together:

1/25 • 12 • 27 = (1/25) * 12 * 27 = 12 * 27 / 25 = 324 / 25.

So the final result is 324 / 25.