Laws of Exponents Review

​Laws of Exponents Review

You might want your notes out to help you!

PRODUCT RULE!

• Keep the base and add the exponents.

Multiple Choice

Simplify the expression:

$$\left(x^3\right)\left(x^7\right)$$  

• $$x^{10}$$  

• $$x^{21}$$  

• $$x^4$$  

• $$10x^{10}$$  

Multiple Choice

Simplify the expression:

$$\left(w^4y^7\right)\left(w^3y^2\right)$$  

• $$wy^5$$  

• $$w^{12}y^{14}$$  

• $$w^7y^9$$  

• $$wy^{16}$$  

PRODUCT RULE with Coefficients

• Multiply the coefficients

• Add the exponents

Multiple Choice

Simplify the expression:

$$8g^3\ \cdot\ 4g^6$$  

• $$12g^9$$  

• $$32g^9$$  

• $$32g^{18}$$  

• $$12g^3$$  

Multiple Choice

Simplify the expression:

$$\left(2a^4b^3\right)\left(4a^5b^2\right)$$  

• $$6ab^{14}$$  

• $$8a^{20}b^6$$  

• $$6a^9b^5$$  

• $$8a^9b^5$$  

QUOTIENT RULE!

• Keep the base and subtract the exponents

Multiple Choice

Simplify the expression:

$$\frac{h^{15}}{h^{11}}$$  

• $$h^{26}$$  

• $$h^4$$  

• $$h^{165}$$  

• $$h^5$$  

Multiple Choice

Simplify the expression:

$$\frac{m^5n^8}{m^3n^4}$$  

• $$m^2n^4$$  

• $$m^8n^{12}$$  

• $$m^{10}n^{12}$$  

• $$m^2n^2$$  

QUOTIENT RULE with Coefficients

• Divide or simplify the coefficients

• Subtract the exponents

Multiple Choice

Simplify the expression: $$\frac{20g^{15}}{5g^3}$$  

• $$4g^{12}$$  

• $$15g^{12}$$  

• $$4g^5$$  

• $$25g^{18}$$  

Multiple Choice

Simplify the expression: $$\frac{4a^{11}b^{15}}{12a^{11}b^{10}}$$  

• $$3b^5$$  

• $$\frac{ab^5}{3}$$  

• $$3ab^5$$  

• $$\frac{b^5}{3}$$  

POWER TO A POWER RULE!

• Keep the base and multiply the exponents!

Multiple Choice

Simplify the expression: $$\left(y^2\right)^4$$  

• $$y^{24}$$  

• $$y^2$$  

• $$y^6$$  

• $$y^8$$  

Multiple Choice

Simplify the expression: $$\left(a^5b^9\right)^{11}$$  

• $$a^{16}b^{20}$$  

• $$a^{55}b^{99}$$  

• $$a^6b^2$$  

• $$a^{154}b$$  

POWER OF A PRODUCT RULE!

• Raise each factor to the exponent

Multiple Choice

Simplify each expression: $$\left(x^5y^7\right)^8$$  

• $$x^{13}y^{15}$$  

• $$x^{40}y^{56}$$  

• $$x^3y$$  

• $$x^{40}y$$  

Multiple Choice

Simplify the expression: $$\left(4m^{10}n^5\right)^2$$  

• $$8m^{20}n^{10}$$  

• $$16m^{20}n^{10}$$  

• $$16m^{12}n^7$$  

• $$6m^{12}n^7$$  

POWER OF A QUOTIENT RULE!

• Raise dividend and divisor to the same exponent!

Multiple Choice

• $$\frac{a^{48}}{b^{16}}$$  

• $$\frac{a^{16}}{b^8}$$  

• $$a^{32}$$  

• $$a^{48}b^{16}$$  

Multiple Choice

• $$x^7y^8z^{10}$$

• $$\frac{x^7y^8}{z^{10}}$$

• $$\frac{x^{10}y^{15}}{z^{25}}$$

• $$\frac{xy^{25}}{z^{25}}$$

ZERO POWER RULE!

• Any number or variable raised to the power of zero is equal to 1

Multiple Select

Choose all expressions that would equal 1.

• $$\left(a^5b^{15}\right)^0$$

• $$\frac{g^0}{h^8}$$

• $$\frac{xy^0}{z^0}$$

• $$\left(h^0\right)\left(g^6k^5\right)^0$$

• $$5m^0n^0$$