Question

1) (4y^5)^4 2) y^23: y^14 3) xy^2z^3 (-2x^2 zy^3) 4) (-2x^5)^4 5) (a^7:a^2)•a^3

Answer 1

Ответ:

1)=4y^20

2)=y^9

3)=-2x^3y^5z^4

4)=16x^20

5)=a^8

Answer 2

Let's simplify each expression step by step:

1. (4y^5)^4

To simplify this, we need to raise both the base (4) and the exponent (5) to the power of 4:

(4^4)(y^(5*4)) (256)(y^20)

So, the simplified expression is 256y^20.

2. y^23 ÷ y^14

When dividing with the same base, you subtract the exponents:

y^(23-14) y^9

The simplified expression is y^9.

3. xy^2z^3 * (-2x^2 zy^3)

To simplify this, we multiply the coefficients and add the exponents for each variable:

xy^2z^3 * (-2x^2 zy^3) = -2x^(1+2) * y^(2+3) * z^(3+1) -2x^3 * y^5 * z^4

So, the simplified expression is -2x^3y^5z^4.

4. (-2x^5)^4

To simplify this, we need to raise both the base (-2) and the exponent (5) to the power of 4:

((-2)^4)(x^(5*4)) (16)(x^20)

So, the simplified expression is 16x^20.

5. (a^7 ÷ a^2) * a^3

When dividing with the same base, you subtract the exponents:

(a^(7-2)) * a^3 a^5 * a^3

When multiplying with the same base, you add the exponents:

a^(5+3) a^8

So, the simplified expression is a^8.

Final Answers:

1. (4y^5)^4 = 256y^20
2. y^23 ÷ y^14 = y^9
3. xy^2z^3 * (-2x^2 zy^3) = -2x^3y^5z^4
4. (-2x^5)^4 = 16x^20
5. (a^7 ÷ a^2) * a^3 = a^8