Maths

[ImagineDragons]

1. Simplify using only positive exponents:

(2t)⁻⁶

2. Simplify using only positive exponents:

(w⁻²j⁻⁴)⁻³(j⁷j³)

3. Simplify using only positive exponents:

a²b⁻⁷c⁴
----------
a⁵b³c⁻²

4. Evaluate the expression for m = 2, t = -3, and z = 0.

z⁻ᵗ(mᵗ)ᶻ

5. Use scientific notation to rewrite the number:
a. 0.0002603 in scientific notation
b. 5.38 × 102 in standard notation

6. The speed of sound is approximately 1.2 × 10³ km/h.
How long does it take for sound to travel 7.2 × 10²
km? Write your answer in minutes.

7. Evaluate the function below over the domain {-1, 0,
1, 2}. As the values of the domain increase, do the
values of the function increase or decrease?

y = (3/4)ˣ

8. Suppose an investment of $5,000 doubles every 12
years. How much is the investment worth after 36
years? After 48 years?
Write and solve an exponential equation.

9. Does the function represent exponential growth or
exponential decay? Identify the growth or decay
factor.

= 9 ∙ (1/2)ˣ

10. You deposit $520 in an account with 4% interest
compounded monthly. What is the balance in the
account after 5 years?

So how do I do these? I remember exponents but not very well.

[Prudie]

You are joking, that's loads.
Hint - anything with a negative exponent can be expressed with positives by taking the reciprocal (ie 1 over it)
For example (2t)⁻⁶ = 1/(2t)⁶

[Buenchico]

A negative power just means the reciprocal of the same expression with a positive power:
http://www.bbc.co.uk/schools/gcsebitesize/maths/number/powersrootshirev3.shtml

With that knowledge you should easily be able to answer the first 4 questions.

[fiction-factory]

Yes, the first one is as prudie says. It can also be written as 1/(64t⁶) although you don't need the bracket if you set it out in the right way.
Have a go at some of the others and we'll check your answers.
Many of these- e.g. Numbers 5 and 8 - are just a straightforward GCSE maths questions so maybe get those out of the way first.