Laws of Exponents Review

Product Law

100

x^4*x^5

x⁹

200

a^4*a^4*a^3

a¹¹

300

(2b^2)(4b^8)

8b¹⁰

400

c^2d^3*cd^2

c³d⁵

500

(3x^3y^4z^2)(-3xy^3z^-1)

-9x⁴y⁷z

Powers Law

100

(x^4)^3

x¹²

200

(a^3b^4)^2

a⁶b⁸

300

(3x^4y^3)^5

243x²⁰y¹⁵

400

(2a^4b^2c)^3

8a¹²b⁶c³

500

((2m^3n^-2p^2)^3)^2

64m¹⁸n^-12p¹²

Quotient Law

100

(a^12)/(a^4)

a⁸

200

(b^3)/(b^-2)

b⁵

300

(x^5y^7)/(x^2y^3)

x³y⁴

400

(12a^4)/(2a)

6a³

500

(32x^4y^5z^8)/(-4xy^2z^3)

-8x³y³z⁵

Mixed Review

100

(a^4*a^3)^2

a⁴⁹

200

(b^3*b^3)/(b^2)

b⁴

300

(4abc)^2(-3a^2bc^3)^2

144a⁵b⁴c⁸

400

((w^3x^4y^-2)/(wx^2z^-4))^3

w⁶x⁶z⁶

500

((2x^3y^-2)(-4xy^4))/(-2xy^2)^2

4x²y^-2

Laws

100

What is the short cut for multiplying exponent terms with common bases?

Add the exponents.

200

What is the short cut for calculating a power to a power?

Multiply the exponents.

300

What is the shortcut for dividing terms with common bases?

Subtract the exponents.

400

If a variable has no exponent, what can you assume?

There is actually an exponent of 1.

500

What is the result when an exponent is 0 (zero)?

Anything to the power of 0 (zero) equals 1.

4⁰=1        48⁰=1            38475⁰=1

x⁰=1         y⁰=1             (4x²y)⁰=1