**If x² = y**³ ,** for what value of z does** = ?

**Answer:**

z= 2

**Step-by-step explanation:**

To solve the question given, we will follow the steps below;

= -----------------------------------------------------------------(1)

but applying the law of indices mᵃᵇ = (mᵃ)ᵇ

then

=

replace by in equation (1)

=

= --------------------------------------------------------------------(2)

but from the question x² = y³

replace y³ by x² in equation (2)

=

=

=

3z = 6

divide both-side of the equation by 3

3z/3 = 6/3

On the left-hand side of the equation, 3 at the numerator will cancel-out 3 at the denominator leaving us with just z while on the right-hand side of the equation 6 will be divided by 3

z= 2

**Answer:**

10 months

$500

**Step-by-step explanation:**

Option 1

- 300 + 20x, where x is the number of months

Option 2

Both options reveal same amount:

- 300 + 20x = 100 + 40x
- 300 - 100 = 40x - 20x
- 200 = 20x
- x = 200/20
**x= 10 months**

Cost of notebook:

- 300 + 20*10 = 300 + 200 =
** $500**

**Answer:**

Your answer is exactly 120 feet