notice: the exponent only applies to what comes directly before it.
5x³ means 5*x*x*x (2x)³ means (2x)*(2x)*(2x)
examples:
write each of the following in expanding form.
13. 5x² 14. 3x⁵ 15. -4x³
16. (2x)³ 17. (-4x)² 18. (-7x)⁵
evaluate the following if x = 3 and y = -2.
19. (2x)³ 20. (-3y)² 21. (5x)²
22. 4(3y)² 23. -5(3x)³ 24. 3(5xy)²

Question

Accepted Answer

# Explanation:
## Step1: Substitute $x = 3$ into $(2x)^3$
$(2\times3)^3$
## Step2: Calculate $2\times3$
$6^3$
## Step3: Calculate $6^3$
$6\times6\times6=216$

## Step1: Substitute $y=-2$ into $(-3y)^2$
$(-3\times(-2))^2$
## Step2: Calculate $-3\times(-2)$
$6^2$
## Step3: Calculate $6^2$
$6\times6 = 36$

## Step1: Substitute $x = 3$ into $(5x)^2$
$(5\times3)^2$
## Step2: Calculate $5\times3$
$15^2$
## Step3: Calculate $15^2$
$15\times15=225$

## Step1: Substitute $y=-2$ into $4(3y)^2$
First, calculate $3y=3\times(-2)=-6$, then $(-6)^2 = 36$, and $4\times36$
## Step2: Calculate $4\times36$
$144$

## Step1: Substitute $x = 3$ into $-5(3x)^3$
First, calculate $3x=3\times3 = 9$, then $9^3=9\times9\times9 = 729$, and $-5\times729$
## Step2: Calculate $-5\times729$
$-3645$

## Step1: Substitute $x = 3$ and $y=-2$ into $3(5xy)^2$
First, calculate $5xy=5\times3\times(-2)=-30$, then $(-30)^2=900$, and $3\times900$
## Step2: Calculate $3\times900$
$2700$

# Answer:
19. $216$
20. $36$
21. $225$
22. $144$
23. $-3645$
24. $2700$

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QUESTION IMAGE

Question

Explanation:

Step1: Substitute \(x = 3\) into \((2x)^3\)

Step2: Calculate \(2\times3\)

Step3: Calculate \(6^3\)

Step1: Substitute \(y=-2\) into \((-3y)^2\)

Step2: Calculate \(-3\times(-2)\)

Step3: Calculate \(6^2\)

Step1: Substitute \(x = 3\) into \((5x)^2\)

Step2: Calculate \(5\times3\)

Step3: Calculate \(15^2\)

Step1: Substitute \(y=-2\) into \(4(3y)^2\)

Step2: Calculate \(4\times36\)

Step1: Substitute \(x = 3\) into \(-5(3x)^3\)

Step2: Calculate \(-5\times729\)

Step1: Substitute \(x = 3\) and \(y=-2\) into \(3(5xy)^2\)

Step2: Calculate \(3\times900\)

Answer: