ALG Unit 6 Day 5- Days 1-4 Refresher

Laws of Exponents Review

What is an exponent?

A simplified notation for repeated multiplication of the same number, term, or variable.

When multiplying, ADD the exponents and keep the same base.

Multiple Choice

Simplify to an equivalent expression BUT leave in exponent form.

4³ ⋅ 4⁵

• 4⁸

• 16⁸

• 4¹⁵

• 16¹⁵

Multiple Choice

Simplify:

b² ⋅ b⁴

• b⁸

• b⁶

• b²

• 2b⁶

When dividing, SUBTRACT the exponent in the denominator (bottom) and keep the base.

Multiple Choice

According to exponent rules, when we divide with the same base we _______ the exponents.

• Multiply

• Add

• Divide

• Subtract

Basics of Negative exponents

By: Ms. Alia Cerda

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Review:

What do you remember about negative exponents?

Negative exponents in the numerator get moved to the denominator and become positive exponents.

Ex: 6^-4 = 1/6⁴

Negative exponents in the denominator get moved to the numerator and become positive exponents.

Ex: 1/6^-4 = 6⁴/1 or 6⁴

Multiple Choice

Rewrite the following expression with a positive exponent:

7^-10

• 7¹⁰

• 1/7^-10

• 1/7¹⁰

• 7/10

Multiple Choice

Rewrite the following expression with a positive exponent: 32^-4

• 1/32^-4

• 32/4

• 32/1

• 1/32⁴

When you have an exponent raise to an exponent, MULTIPLY the exponents.

Multiple Choice

According to exponent rules, when we raise a power to another exponent we _______ the exponents.

• add
• subtract
• multiply
• divide

Multiple Choice

Simplify:

(x⁵)⁴

• x⁹

• x²⁰

• x

• x⁵⁴

Anything with a power/exponent of zero equals 1!

Multiple Choice

Simplify (-1/2)⁰

• 1

• 0

• -1

• -2

Multiple Choice

Which expression is equivalent to $$\frac{12x^6y^{-4}z^2}{3x^2y^{-6}z^3}$$   for all values of x, y, and z where the expression is defined?

• $$\frac{9x^8z^5}{y^{-10}}$$  

• $$\frac{4x^8z^5}{y^{-10}}$$  

• $$\frac{9x^4y^2}{z}$$  

• $$\frac{4x^4y^2}{z}$$  

Multiple Choice

A rectangular prism has a width of $$x$$ inches, a length of $$x^2y$$ inches, and  height of $$y^2$$  inches. Which expression represents the volume in cubic inches of this rectangular prism?

• $$4x^2y^2$$  

• $$4x^3y^3$$  

• $$x^2y^2$$  

• $$x^3y^3$$  

Multiple Choice

Which expression is equivalent to $$\frac{14a^4b^6c^{-10}}{8a^{-2}b^3c^{-5}}$$   for all values of a, b, and c where the expression is defined?

• $$\frac{7a^2b^3}{4c^{15}}$$  

• $$\frac{6a^2b^9}{c^{15}}$$  

• $$\frac{7a^6b^3}{4c^5}$$  

• $$\frac{7b^2c^2}{4a^2}$$  

Multiple Choice

Which expression is equivalent to $$\left(144k^2r^{14}\right)^{\frac{1}{2}}$$  for all positive values of  k and r ?

• $$12kr^7$$  

• $$72k^2r^{14}$$  

• $$144kr^7$$  

• $$12k^2r^{14}$$  

Multiple Choice

Which expression is equivalent to $$\frac{\left(q^4\right)^{-3}}{q^{-15}}$$  for all values of  where the expression is defined?

• $$q^{27}$$  

• $$\frac{1}{q^{27}}$$  

• $$q^3$$  

• $$\frac{1}{q^3}$$  

Multiple Choice

Which expression is equivalent to $$\frac{x^2y^5}{6z^3}\cdot\frac{2z}{3x^3y^4}$$  ?

• $$\frac{y}{9xz^2}$$  

• $$\frac{y}{16xz^2}$$  

• $$\frac{x^5y^9z^4}{9}$$  

• $$\frac{x^5y^9}{4z^4}$$  

Multiple Choice

. which expression is equivalent to $$\left(5a^2\right)\left(3a^7\right)$$  ?

• $$8a^{14}$$  

• $$15a^{14}$$  

• $$8a^9$$  

• $$15a^9$$  

Multiple Choice

which expression is equivalent to $$\left(-3a^3\right)^2\left(2ab\right)^4$$  ?

• $$-48a^{10}b^4$$  

• $$-54a^{10}b^4$$  

• $$72a^{10}b^4$$  

• $$144a^{10}b^4$$  

Multiple Choice

Which expression is equivalent to $$\frac{18a^4}{3a}$$  ?

• $$15a^3$$  

• $$6a^5$$  

• $$6a^3$$  

• $$21a^5$$  

Multiple Choice

which expression is equivalent to $$3a^2b^{-3}$$  ?

• $$\frac{b^3}{3a^2}$$  

• $$\frac{3a^2}{b^{-3}}$$  

• $$\frac{3b^3}{a^2}$$  

• $$\frac{3a^2}{b^3}$$  

Multiple Choice

Which expression is equivalent to $$\left(4x^5y\right)^3$$  ?

• $$12x^8y^3$$  

• $$64x^{15}y^3$$  

• $$12x^{15}y$$  

• $$12x^8y$$  

Multiple Choice

Which is equivalent to $$5y^3+4y^3$$  ?

• $$20y^9$$  

• $$20y^3$$  

• $$9y^3$$  

• $$9y^6$$