Powers

Question 1

Powers: Basic Rules - Raising a Power to Another Power

Answer 1

When raising a power to another power, multiply the exponents.

For example:

(a^m)^n = (a^n)^m = a^m·n

The equation works both ways:

a6 can be split up to a^3⋅2, which can then be rewritten as the equivalent (a^3)2 or (a^2)3, as needed by the question.

Question 2

Powers: Basic Rules - Negative Exponents

Answer 2

Powers: Basic Rules - Negative Exponents

Negative exponents signify a reciprocal relation. Anything raised to a negative exponent becomes
1 / [the original power without the negative sign]

a^−n = 1 / a^n

Question 3

Powers: Scientific Notation

Answer 3

Scientific notation: a×10n where a (the digit term) indicates the number of significant figures in the number and 10n (the exponential term) places the decimal point.

A positive exponent shows that the decimal point is shifted that number of places to the right.
A negative exponent shows that the decimal point is shifted that number of places to the left.
The rule: Maintain the balance between the digit term and the exponential term. If one goes up (↑) by a magnitude of 10, the other must go down (↓) by the same magnitude, and vice versa.

Question 4

Powers: Exponential Equations

Answer 4

Identifying exponential equations - an equation with variables in the exponents.

Solving the problem (3-step process):

1) Bring both sides of the equation to the same base(s).
2) Ignore the bases and equate the exponents.
3) Solve for the needed variables.

Question 5

Plugging In - DOZEN F

Answer 5

Make sure your answer is always true by plugging in DOZEN F. These numbers, in turn, cause the answers to behave differently, exposing the sometimes answers while leaving only the always true answer. Some of these numbers overlap with the bad numbers.
Remember the DOZEN F:

Different (e.g. even vs. odds, prime vs. multiple, fractions vs. integers, positive vs. negative, etc.)
One
Zero
Equal numbers for different variables
Negatives
Fractions

Question 6

Powers: Reverse Rules - Multiplying Powers with the same Base

Answer 6

Explain what is stated in the passage concerning a specific detail.

Specific. Locate the detail in the passage, using the Initial Reading to point to the paragraph in which the detail is most likely to be found.

Stated. You are asked to describe what is explicitly said in the passage concerning this detail.

Beware of (a) answer choices containing details that appear elsewhere in the passage; (b) distortions of the detail (replacing hill with mountain, etc.).

Look for (a) synonyms (replacing die with perish); (b) different word order, same meaning.

Common phrasing:

1. Which of the following is mentioned in the passage (about…)?
2. According to the passage…
3. Which statement about… is supported by information in the passage?