EVALUATING EXPRESSIONS WITH EXPONENTS

To evaluate the given expressions with exponents, we have to be clear with the following concepts.

  • Order of operations
  • About exponents
  • Operations with exponents
  • Operations with numbers

Evaluate the following :

Example 1 :

a + b2(b-a) if a = 5 and b = -3

Solution :

Given :

= a + b2(b-a)

By applying the values of a and b, we get

= 5 + (-3)2(-3-5)

= 5 + 9(-8)

= 5 - 72

= -67

So, the answers is -67.

Example 2 :

(x4-3wy)/(y3+2w) if w= 4, x = -3 and y = -5.

Solution :

Given :

= (x4-3wy)/(y3+2w)

By applying the values of w, x and y, we get

w = 4, x = -3 and y = -5

= (44-3(4)(-5)) / ((-5)3+2(4))

= (44+60) / (-125+8)

= (256+60) / (-117)

= -316/117

So, the answer is -316/117.

Example 3 :

h2k + h(h-k) if h = 4, k = 1/2

Solution :

= 42(1/2) + 4(4-(1/2))

= (16/2) + 4(7/2)

= 8 + 14

=  22

So, the answer is 22.

Example 4 :

A player's attack percentage A is calculated using the formula 

A = (k - e)/t

where k represents the number of kills, e represents the number of heart attack errors including blocks, and t represents the total attacks attempted. Find the attack percentage when k = 22, e = 11and t = 35.

Solution :

A = (k - e)/t

when k = 22, e = 11and t = 35

A = (22-11)/35

A = 11/35

A = 0.314

So, the players attack percentage is 0.314%.

Example 5 :

Evaluate

5(d+a)/2ab2

when a = -4, b = 1/2, and d = 1/5

Solution :

Given :

= 5(d+a)/2ab2

By applying the given values, we get

= 5(1/5 + (-4)) / 2(-4) (1/2)2

= 5(-19/4) / (-2)

= 95/8

Example 6 :

The formula for the volume V of a cone with radius r and height

h = 1/3 πr2h

Write the expressions for the volume of the cone given below. 

Solution :

From the picture given above,

diameter = 6x, radius = 3x and height = 2x

V = (1/3) πr2h

V = (1/3)π(3x)2(2x)

V = (1/3)π(9x)(2x)

V = 6x2π

Example 7 :

The average price for a movie ticket can be represented by 

P = y2/400 + 7y/100 + 2.96

where y is the number of years since 1980.

(a) Find the average price of a ticket in 1990.

Solution :

P = y2/400 + 7y/100 + 2.96

y = 1990

P = (1990)2/400 + 7(1990)/100 + 2.96

P = 9900.25 + 139.3 + 2.96

P = 2132.51

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