1. ## Homework Problems

Any help with the following three homework questions would be appreciated:
Make T the subject:
E = 800(T – 20)

Simplify
(2pq3)4

2pq to the power of 3 to the power of 4

Evaluate
5-2 x 1000.5

Five to the power of minus 2 x 100 to the power of 0.5

Apologies for not being sure which form topic to put these questions under. Any help would be greatly appreciated.

2. Originally Posted by Damtol
Any help with the following three homework questions would be appreciated:
Make T the subject:
$\displaystyle E = 800(T - 20)$
Hi Damtol,

For this one, we need to distribute the 800 and then isolate T.

$\displaystyle E = 800(T- 20)$

$\displaystyle E=800T-16000$

$\displaystyle 800T=E+16000$

$\displaystyle T=\frac{E+16000}{800}$

$\displaystyle T=\frac{E}{800}+20$

Originally Posted by Damtol
Simplify

$\displaystyle (2pq^3)^4$
$\displaystyle 16p^4q^{12}$

Remember $\displaystyle (x^a)^b=x^{ab}$

Originally Posted by Damtol

Evaluate
$\displaystyle 5^{-2}(100)^{.5}$

$\displaystyle \frac{1}{5^2} \cdot 100^{1/2}$

$\displaystyle \frac{1}{25} \cdot 10=\frac{2}{5}$

Apologies for not being sure which form topic to put these questions under. Any help would be greatly appreciated.

3. Originally Posted by Damtol
Any help with the following three homework questions would be appreciated:
Make T the subject:
E = 800(T – 20)

Simplify
(2pq3)4

2pq to the power of 3 to the power of 4

Evaluate
5-2 x 1000.5

Five to the power of minus 2 x 100 to the power of 0.5

Apologies for not being sure which form topic to put these questions under. Any help would be greatly appreciated.

E = 800(T – 20)

E=800T-16000

T=(E+16000)/800

$\displaystyle (2pq)^3=8p^3q^3$

$\displaystyle (8p^3q^3)^4=8^4p^{12}q^{12}$

$\displaystyle 5^{-2}\times100^{0.5}$

$\displaystyle \frac{1}{25}\times10=Ans$

4. Originally Posted by Damtol
1) Make T the subject:
E = 800(T – 20)
To learn the general techniques for solving literal equations, try here.

For this particular exercise, a good first step is to multiply through, to get the "T" outside the parentheses:

. . . . .$\displaystyle E\, =\, 800T\, -\, 1600$

Then add the 1600 to either side of the equation, and divide through by 800.

Originally Posted by Damtol
Simplify

2) (2pq3)4

2pq to the power of 3 to the power of 4
Your formatting is unclear; I will guess that you mean the following:

. . . . .$\displaystyle \mbox{2) }\, (2pq^3)^4$

To learn exponent rules, try here. For examples of how to simplify, try here.

Once you're familiar with the background material, the following should make sense:

. . . . .$\displaystyle (2pq^3)^4\, =\, (2)^4\, (p)^4\, (q^3)^4\, =\, (16)(p^4)\left(q^{3 \times 4}\right)$

...and so forth.

Originally Posted by Damtol
Evaluate

3) 5-2 x 1000.5

Five to the power of minus 2 x 100 to the power of 0.5
So the expression is as follows...?

. . . . .$\displaystyle 5^{-2}\, \times\, 100^{0.5}$

If so, note that 0.5 = 1/2 and that fractional exponents can be stated as radicals:

. . . . .$\displaystyle 5^{-2}\, \times \, \sqrt{100}$

Then note that negative exponents tell you to move the base to the other side of the fraction line:

. . . . .$\displaystyle \frac{1}{5^2}\, \times\, \sqrt{100}$

Simplify, and you're done!

5. Thanks for the replies and help given; this has become a lot clearer. Once again thanks everyone.