Question

Запишите в виде одночлена стандартного вида a)5x²yz²×(-3yxz²) b)-8a⁷b⁵c⁴÷(-2a³cb²)²​

Answer 1

$a)5 {x}^{2} y {z}^{2} \times (-3yx {z}^{2}) = - 15 {x}^{3} {y}^{2} {z}^{4}$

$b) - \frac{8 {a}^{7} {b}^{5} {c}^{4} }{ {( - 2 {a}^{3} c {b}^{2}) }^{2} } = - \frac{8 {a}^{7} {b}^{5} {c}^{4} }{4 {a}^{6} {c}^{2} {b}^{4} } = - 2 ab {c}^{2}$

Answer 2

a) 5x²yz² × (-3yxz²)

To simplify this expression, we can use the properties of exponents and the multiplication of variables.

First, let's simplify the numerical coefficients: 5 × (-3) = -15.

Next, let's multiply the variables with the same bases. In this case, we have x, y, and z.

For the x term, we have x² × (-yx) = -xy³.

For the y term, we have yz² × y = y³z².

For the z term, we have z² × z² = z⁴.

Combining all these terms, we get: -15xy³z⁴.

Therefore, the simplified form of the expression 5x²yz² × (-3yxz²) is -15xy³z⁴.

b) -8a⁷b⁵c⁴ ÷ (-2a³cb²)²

To simplify this expression, we can use the properties of exponents and division of variables.

First, let's simplify the numerical coefficient: -8.

Next, let's simplify the variables.

For the a term, we have a⁷ ÷ (a³)² = a⁷ ÷ a⁶ = a.

For the b term, we have b⁵ ÷ (b²)² = b⁵ ÷ b⁴ = b.

For the c term, we have c⁴ ÷ (c)² = c⁴ ÷ c² = c².

Combining all these terms, we get: -8ab²c².

Therefore, the simplified form of the expression -8a⁷b⁵c⁴ ÷ (-2a³cb²)² is -8ab²c².