Question

Приведите одночлен к стандартному виду: 1) (2a^2)*1/4a^2 2)(-3b^4)^5*1/27b^3 3)(-5a^3b^2)^2*(-0,2a^2b^3)^-1

Answer 1

1) (2a²)*1/4 a² = 1/2 a⁴ = 0,5a⁴
2) (-3b⁴)⁵ * 1/27 b³ = -3⁵b²⁰ * 3⁻³ b³ = -9b²³
3) (-5a³b²)² *(-0,2a²b³)⁻¹ = -25a⁶b⁴ * 5a⁻²b⁻³ = -125a⁴b³

Answer 2

1. (2a^2)*1/4a^2 = 1/2

To simplify this expression, we can cancel out the common factor of 4a^2 from the numerator and denominator of the fraction, which leaves us with:

(2a^2) * (1/4a^2) = (2/4) = 1/2

So the standard form of this expression is simply 1/2.

2. (-3b^4)^5*1/27b^3 = -243b^17/27

To simplify this expression, we can first apply the exponent to the base of the first term, which gives us:

(-3b^4)^5 = (-3)^5 * (b^4)^5 = -243b^20

Next, we can simplify the fraction by canceling out the common factor of 27 from both the numerator and denominator, which gives us:

(-243b^20)/(27b^3) = -9b^17

So the standard form of this expression is -9b^17.

3. (-5a^3b^2)^2*(-0,2a^2b^3)^-1 = 12,5a^-4b^-1

To simplify this expression, we can first apply the exponent to the base of the first term, which gives us:

(-5a^3b^2)^2 = 25a^6b^4

Next, we can simplify the second term by taking the reciprocal of it and changing the sign of the exponent, which gives us:

(-0,2a^2b^3)^-1 = (-1)/(0,2a^2b^3) = -5a^-2b^-3

Then, we can multiply these two terms together to get:

(25a^6b^4)*(-5a^-2b^-3) = -125a^4b

Finally, we can simplify this expression by rearranging the terms and dividing out any common factors of a and b, which gives us:

-125a^4b = -12,5a^-4b^-1

So the standard form of this expression is -12,5a^-4b^-1.