Understanding Exponents

Question 1

Write (3b^3)^2 without exponents.

Answer 1

The exponent 2 tells us how many times 3b^3 appears in the product.
Then each exponent of 3 tells us how many b’s to multiply.
Answer: 3bbb3bb*b

Question 2

Evaluating an expression with a negative exponent: Negative integer base

Answer 2

For any non-zero number and any whole number , we have the following. a^-n = 1/a^n

Question 3

Rewriting an algebraic expression w/o a negative exponent. Explanation: For any non-zero number a and any whole number n, we have the following…

Answer 3

Rule 1: a^-n = 1/a^n or Move a^-n to the denominator and make the exponent positive.

Example rule 1: -3m^-4 = -3/m^4
The whole number stays in the numerator but the variable changes places. This applies to both rules

Rule 2: 1/a^-n = a^n or Move a^-n to the numerator and make the exponent positive

Example rule 2: 1/6x^-2 = (x^2)/6

Question 4

Product Rule

Answer 4

x^rx^s = x^r+s Example x^3x^5 = x^8

Question 5

Quotient Rule

Answer 5

x^r/x^s = x^r-s Example a^6/a^2 = a^4

Question 6

Power of a power rule

Answer 6

(x^r)^s = x^r*s Example (z^2)^5 = z^10

Question 7

Power of a product rule

Answer 7

(xy)^r = x^ry^r Example (ab)^2 = a^2b^2

Question 8

Power of a quotient rule

Answer 8

(x/y)^r = x^r/y^r Example (5/7)^3 = 5^3/7^3

Question 9

Write .00000653 in scientific notation

Answer 9

To do this, we first move the decimal point until we get a number between 1 and 10.
We get 6.53
Since we had to move the decimal point six places to the right, we multiple 6.53 * 10^-6

Question 10

Write 2.8 x 10^4 in standard notation.

Answer 10

Note that it is written in scientific notation.
It has a number between 1 and 10 multiplied by a power of ten.
To write it in standard notation, we do the multiplication. 2.8 x 10,000 = 28,000