Question

1) 5^-4*5^2 2)(а^-5)^4*а^22 3) (1\6х^-4*у^3)^-1*(3а^-4\2b-3)^-2*10а^7b^3

Answer 1

1)5^-4+2=5^2=25
2)а^-5*4*а^22=а^-20*а^22=а^2
3) не успеваю я сам на уроке)

Answer 2

Let's simplify the given expressions step by step:

1. $5^{-4} \cdot 5^2$:

When you multiply two terms with the same base and different exponents, you can add the exponents:

$5^{-4} \cdot 5^2 = 5^{-4+2} = 5^{-2} = \frac{1}{5^2} = \frac{1}{25}$.

2. $(a^{-5})^4 \cdot a^{22}$:

When you raise a power to another power, you multiply the exponents:

$(a^{-5})^4 \cdot a^{22} = a^{-20} \cdot a^{22} = a^{-20+22} = a^2$.

3. $\left(\frac{1}{6}x^{-4} \cdot y^3\right)^{-1} \cdot \left(\frac{3a^{-4}}{2b^{-3}}\right)^{-2} \cdot 10a^7b^3$:

First, let's simplify each part of the expression:

• $\left(\frac{1}{6}x^{-4} \cdot y^3\right)^{-1} = \frac{1}{\frac{1}{6}x^{-4} \cdot y^3} = \frac{6}{x^{-4} \cdot y^3} = 6x^4y^{-3}$.

• $\left(\frac{3a^{-4}}{2b^{-3}}\right)^{-2} = \frac{1}{\frac{3a^{-4}}{2b^{-3}}} = \frac{2b^{-3}}{3a^{-4}} = \frac{2}{3} \cdot \frac{b^{-3}}{a^{-4}} = \frac{2b^{-3}}{3a^{-4}} = \frac{2}{3} \cdot \frac{1}{a^4b^3} = \frac{2}{3a^4b^3}$.

Now we have:

$\left(6x^4y^{-3}\right) \cdot \left(\frac{2}{3a^4b^3}\right) \cdot 10a^7b^3$.

Multiply the constants:

$6 \cdot \frac{2}{3} \cdot 10 = 20$.

Combine the variable terms by adding exponents:

$x^4 \cdot a^7$ and $y^{-3} \cdot b^3$.

So the final expression is $20x^4a^7y^{-3}b^3$