Question

(y⁴)⁵:(y⁹)²ₓ y³ при y=-1 (z³)⁹:(z⁴)⁶ ₓ z при z=-2

Answer 1

$(y^4)^5:(y^9)^2\cdot y^3=y^{20}:y^{18}\cdot y^2=\frac{y^{20}\cdot y^2}{y^{18}}=\frac{y^{22}}{y^{18}}=y^4=(-1)^4=1\\\\(z^3)^9:(z^4)^6\cdot z=z^{27}:z^{24}\cdot z=\frac{z^{27}\cdot z}{z^{24}}=\frac{z^{28}}{z^{24}}=z^4=(-2)^4=16$

Answer 2

To evaluate the given expressions, simply substitute the given values of y and z into the expressions and perform the calculations. Let's start with the first expression:

Expression 1: (y⁴)⁵ / (y⁹)² ₓ y³, where y = -1

Substitute y = -1 into the expression: ((-1)⁴)⁵ / ((-1)⁹)² ₓ (-1)³

Now, calculate the values inside the parentheses: (1)⁵ / (1)² ₓ (-1)³

Calculate the exponents: 1 / 1 ₓ (-1)

Perform the multiplication and division: -1

So, the value of Expression 1 when y = -1 is -1.

Now, let's move on to the second expression:

Expression 2: (z³)⁹ / (z⁴)⁶ ₓ z, where z = -2

Substitute z = -2 into the expression: ((-2)³)⁹ / ((-2)⁴)⁶ ₓ (-2)

Now, calculate the values inside the parentheses: (-8)⁹ / (16)⁶ ₓ (-2)

Calculate the exponents: -134217728 / 16777216 ₓ (-2)

Perform the division and multiplication: -8 ₓ (-2)

Finally, perform the multiplication: 16

So, the value of Expression 2 when z = -2 is 16.