U1, C2, Properties of Exponents

Question 1

Product Property of Exponents

Answer 1

If exponential expressions being MULTIPLIED have the same base, you can ADD the exponents.

3²x3⁶x3 = 3⁹

Because 2 + 6 + 1 = 9

Question 2

Quotient Property of Exponents

Answer 2

Two exponential expressions being divided by eachother, (as long as they share the same base) will allow you to subtract the exponents from eachother.

3⁴/3² is the same as 3^4-2

Which is 3² = 9

Question 3

Power of a Product Property of Exponents

Answer 3

When you have a PRODUCT (numbers being multiplied together) being raised to an exponent, you can simply apply that exponent to each product.

(4x6)^2 = 4^2 x 6^2 = 16 x 36 = 576

Question 4

Power of a Quotient Property of Exponents

Answer 4

Put the exponent on every factor in both the numerator and denominator.

Question 5

Power of a POWER Property of Exponents

Answer 5

When you raise an exponential expression (a^m) and raise it to another exponent, n;

(a^m)ⁿ

You multiply the two exponents together:

(a^m)ⁿ = a^mn

Question 6

Negative Exponents

Answer 6

A negative exponent will equal the resiprocal of the base.

so a^-2 will equal 1/a²

^{When to use?}

^{Whenever you have a negative exponent, you need to basically move it to the resiprocal. aka, if its in the numerator, move to denominator & vice versa}

Question 7

Inverse Operations - Radicals & Exponents

Answer 7

Just as multiplication and division are inverse operations of one another, radicals and exponents are also inverse operations.

For example, suppose we have the the number 3 and we raise it to the second power. Now if we were to take the square root of 32, notice that we will end up with 3. This is the number with which we started.

Question 8

Fractional Exponents and Radicals /

How do you simplify a radical containing an exponential expression, where the index does not match the exponent?

eg, the cube root of two to the fifth power

index = 3, exponent = 5

Answer 8

You can simplify any radical of any index by raising it to the power of the resiprocal of the radical’s index.

eg, anything that is cubed can be raised to the 1/3 power to cancel out the radical.

So, the cube root of 2 to the 5th power would be raised to the 1/3 power to get rid of the radical, so youd have (2^5)^1/3 and then to simplify, use the power to a power property of exp, giving 2^5/3

Put simply, you can move the index to the denominator and the exponent to the numerator and be done.

Question 9

What is the x root of y to the x power?

Answer 9

y

Question 10

What is x^-y ?

Answer 10

1 / x^y

(the y becomes positive)

Question 11

Product of Powers:

What is a^x x a^y ?

Answer 11

a^x+y

Question 12

Power of a Product Property

What is (ab)ⁿ ?

Answer 12

aⁿ x bⁿ

Question 13

Quotient of Powers Property

What is aⁿ/a^m ?

Answer 13

a^n-m

Question 14

Power of Quotient Property

What is (a/b)ⁿ ?

Answer 14

aⁿ/bⁿ

Question 15

Power of a Power Property

What is (aⁿ)^m ?

Answer 15

a^nm

Question 16

What is scientific notation?

Answer 16

Its a way to express big numbers simplified.

it can be a product of a dec and then times 10 to the power of x, where x is the # of decimal places.

If the # being simplified is an int, x will be raised to a positive power.

If the # being simplified is an dec, x will be raised to a negative power.

So 670000 is 6.7 x 10⁵

and 0.00003 is 3 x 10^-5

You can only have a single non zero digit to the left of the decimal.

You can have as many as you want to the right.

Moving the decimal 1 to the right subtracts 1 from the exponent & vice versa (left 1 = + 1)

Question 17

Product Property of Radicals

Answer 17

The nth root of a times b

is equal to

a to the nth root times b to the nth root

Question 18

Quotent Property of Radicals

Answer 18

The nth root of a over b

is equal to

the nth root of a

over
the nth root of b

Question 19

What is the nth root of A to the n?

Answer 19

A

Question 20

What is the nth root of A to the m?

Answer 20

A^m/n