Question

. Find the value of each expression. Show your work. (a) 1.42 (b) 300 = 2(0.5 +4.5) ? 3 ) te) -23

Answer 1

a. After solving
`1.4^(2)` we get 1.96

b. After solving
`(300/2(0.5+4.5)^(2)\)` we get 6.

c. After solving
`[(1)/(3)/2\cdot((1)/(2))^(3)]` we get
`(4)/(3)`.

(a)
`(1.4^(2))`

To solve this expression, we simply square the number 1.4.

`1.4^(2)` = (1.4)(1.4)

`1.4^(2)` = 1.96

(b)
`(300/2(0.5+4.5)^(2)\)`

To solve this expression, we first need to evaluate the parentheses inside the parentheses.

`(0.5+4.5)^(2)` =
`(5)^(2)` = 25

Now we can plug this value into the expression and solve it.

`300/2(0.5+4.5)^(2)` =
`300/2(25)`

=
`300/50`

= 6

(c)
`[(1)/(3)/2\cdot((1)/(2))^(3)]`

To solve this expression, we need to work from the inside out. First, we evaluate the exponent in the parentheses.

`((1)/(2))^(3) = (1)/(2)\cdot(1)/(2)\cdot(1)/(2)` =
`(1)/(8)`

Now we can plug this value into the expression and solve it.

`(1)/(3)/2\cdot((1)/(2))^(3)` =
`(1)/(3)/2\cdot(1)/(8)` =
`(1)/(3)/(1)/(4)` =
`(4)/(3)`

Answer 2

For the first expression, we have 1.4², this can be expressed as 1.4×1.4 and then we get:

`1.4^2=1.4*1.4=1.96`

For the second expression, 300 ÷ 2(0.5 + 4.5)² we must start by solving the sum inside the parenthesis, then we get:

300 ÷ 2(0.5 + 4.5)² = 300 ÷ 2(5)²

Then, solve the exponent on the right of the division symbol:

300 ÷ 2(5)² = 300 ÷ 2×25

Now, solve the multiplication

300 ÷ 2×25 = 300 ÷ 50

Now, we can solve the division

300 ÷ 50 = 6

Then, 300 ÷ 2(0.5 + 4.5)² = 6

For the last expression, we must start with the exponent:

`\begin{gathered} (1)/(3)/2((1)/(2))^3 \\ (1)/(3)/2*(1)/(2^3) \\ (1)/(3)/2*(1)/(8)^{} \end{gathered}`

Now we can solve the multiplication:

`(1)/(3)/2*(1)/(8)^{}=(1)/(3)/(2)/(8)^{}`

In order to divide one fraction by another one we just have to keep the first fraction unchanged, change the ÷ for a × and flip the second fraction, like this:

`(1)/(3)/(2)/(8)^{}=(1)/(3)*(8)/(2)=(1*8)/(3*2)=(8)/(6)=(4)/(3)`

Then, the value of the last expression is 4/3