Laws of Exponents

Laws of Exponents

Objectives:

1. Simplify expressions using the laws of exponents.

2. Simplify expressions involving parentheses and exponents.

Instruction:

Choose the correct answer on the following problems.

Multiple Choice

Simplify $$5y^3\cdot3y^2$$ .

• $$15y^2$$

• $$15y^3$$

• $$15y^5$$

• $$15y^6$$

Laws of Exponents

Product Rule

Multiple Choice

Simplify $$\left(-2x^3\right)^4$$ .

• $$-16x^7$$

• $$-16x^{12}$$

• $$16x^7$$

• $$16x^{12}$$

Laws of Exponents

Power of a power rule

Multiple Choice

Simplify $$\left(-a^2b^3\right)^2$$ .

• $$a^4b^5$$

• $$a^4b^6$$

• $$-a^4b^5$$

• $$-a^4b^6$$

Laws of Exponents

Power of a Product Rule

Laws of Exponents

ERROR ALERT!

Multiple Choice

Simplify $$\frac{-9r^3s^5}{-6rs^3}$$ .

• $$\frac{3}{2}r^2s^2$$

• $$\frac{3}{2}r^3s^2$$

• $$-\frac{3}{2}r^2s^2$$

• $$-\frac{3}{2}r^3s^2$$

Laws of Exponents

Quotient rule

Multiple Choice

Simplify $$\left(\frac{-2u^4}{-3v^4}\right)^3$$ .

• $$\frac{2}{3}u^3v^3$$

• $$-\frac{2u^7}{3v^7}$$

• $$-\frac{8u^7}{27v^7}$$

• $$\frac{8u^{12}}{27v^{12}}$$

Laws of Exponents

Power of a Quotient rule

Multiple Choice

Simplify $$-6^0x^2y$$ .

• $$xy^3$$

• $$x^2y$$

• $$-x^2y$$

• $$-xy^3$$

Laws of Exponents

Zero Exponent rule

Multiple Choice

Simplify $$-4m^{-3}$$ .

• $$4m^3$$

• $$-\frac{1}{4m^3}$$

• $$-\frac{4}{m^3}$$

• $$\frac{1}{4m^3}$$

Laws of Exponents

Downward Negative Exponent Rule

Multiple Choice

Simplify $$\frac{2^2}{2^{-4}}$$ .

• $$2^2$$

• $$\frac{1}{2^2}$$

• $$\frac{1}{2^6}$$

• $$2^6$$

Laws of Exponents

Upward Negative Exponent Rule

Multiple Choice

Simplify $$\frac{3z^{-2}}{-6y^{-2}}$$ .

• $$-\frac{y^2}{2z^2}$$

• $$\frac{2y^2}{z^2}$$

• $$\frac{y^2}{4z^2}$$

• $$-\frac{4y^2}{z^2}$$

Laws of Exponents

Reciprocal Rule