18April2024 Laws of Exponents

Exponents
Review

Multiple Choice

True or False?

$$3^3=9$$

• True
• False

Multiple Choice

True or False?

$$\left(-2\right)^4=2^4$$

• True
• False

Multiple Choice

True or False?

$$\left(a^2\right)^3=a^5$$

• True
• False

Multiple Choice

True or False?

$$\left(\frac{1}{2}\right)^4=\frac{1}{2^4}$$

• True
• False

Multiple Choice

True or False?

$$-2^2=4$$

• True
• False

Multiple Choice

True or False?

$$2^3\cdot2^4=2^7$$

• True
• False

Multiple Choice

True or False?

$$\left(3x\right)^2=6x$$

• True
• False

Multiple Choice

True or False?

$$\left(-x\right)^2=x^2$$

• True
• False

Power Rule

Multiple Choice

$$t^3\cdot t\cdot t^{15}$$

• $$t^{18}$$

• $$t^{19}$$

Multiple Choice

$$n^5\cdot n^6\cdot n^9$$

• $$n^{20}$$

• $$n^{270}$$

Multiple Choice

$$\left(10a^7\right)\left(-4a^3\right)$$

• 
  $$-100a^{10}$$

• 
  $$-36a^{10}$$

• 
  $$-40a^{10}$$

• 
  $$-14a^{10}$$

Multiple Choice

$$\left(-6p^5\right)\left(-7p^5\right)$$

• 
  $$42p^{10}$$

• $$-42p^{25}$$

Multiple Choice

$$\left(5x^2\right)\left(-2x^3\right)\left(3x^4\right)$$

• $$-30x^9$$

• $$-30x^{24}$$

Multiple Choice

$$3^2+3^3$$

• $$3^5$$

• $$36$$

Multiple Choice

$$2^5+2^{ }$$

• $$2^6$$

• $$34$$

Multiple Choice

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

• $$21r^3$$

• $$343r^3$$

Multiple Choice

$$\left(\frac{1}{2}\right)^3$$

• $$\frac{1}{8}$$

• $$\frac{3}{6}$$

Multiple Choice

$$\left(\frac{a}{b}\right)^3$$

• $$\frac{a^3}{b^3}$$

• $$\frac{3a}{3b}$$

Multiple Choice

$$\left(-\frac{2x}{y}\right)^5$$

• $$-\frac{10x^5}{y^5}$$

• $$-\frac{2^5x^5}{y^5}$$

Multiple Choice

$$\left(-5m^4p^2\right)^3$$

• $$125m^{12}p^6$$

• $$-125m^{12}p^6$$

• $$-125m^7p^5$$

Multiple Choice

$$\left(6x^2y^3\right)^5$$

• $$6^5x^{10}y^{15}$$

• $$30x^7y^8$$

• $$30x^{10}y^{15}$$

Multiple Choice

$$\left(2w^2x^3y\right)^2\left(x^4y\right)^5$$

• $$4w^5x^{10}y^{10}$$

• $$4w^4x^{26}y^7$$

Multiple Choice

$$\left(\frac{5a^2b^5}{c^6}\right)^3,\ c\ne\ 0$$

• $$\frac{15a^6b^{15}}{c^{18}}$$

• $$\frac{125a^5b^8}{c^9}$$

• $$\frac{125a^6b^{15}}{c^{18}}$$

Zero and Negative Exponents

Multiple Choice

$$9^0$$

• -1

• 0

• 1

Multiple Choice

$$-8^0$$

• -1

• 0

• 1

Multiple Choice

$$\left(-4\right)^0-4^0$$

• -1

• 0

• 1

Multiple Choice

$$8^0-12^0$$

• -1

• 0

• 1

Multiple Choice

$$\frac{0^{10}}{12^0}$$

• -1

• 0

• 1

Multiple Choice

$$\frac{0^5}{2^0}$$

• -1

• 0

• 1

Multiple Choice

$$-\left(-13\right)^0$$

• -1

• 0

• 1

Write with positive exponents and simplify. Assume that all variables represent nonzero real numbers.

Multiple Choice

$$2^{-3}$$

• $$-6$$

• $$\frac{1}{2^{-3}}$$

• $$\frac{1}{8}$$

• $$\frac{1}{-6}$$

Multiple Choice

$$\left(\frac{1}{7}\right)^{-2}$$

• $$\left(\frac{1}{7}\right)^2$$

• $$\left(\frac{7}{1}\right)^2$$

Multiple Choice

$$\left(\frac{3}{2}\right)^{-4}$$

• $$\left(\frac{3}{2}\right)^4$$

• $$\left(\frac{2}{3}\right)^4$$

Multiple Choice

$$a^{-4}$$

• $$a^4$$

• $$\frac{1}{a^4}$$

• $$-\frac{1}{a^4}$$

Multiple Choice

$$x^{-6}y^3$$

• $$\frac{y^3}{x^6}$$

• $$\frac{x^6}{y^3}$$

Multiple Select

$$\frac{5^{-3}}{6^{-2}}$$

• $$\frac{6^3}{5^2}$$

• $$\frac{6^2}{5^3}$$

• $$\frac{36}{125}$$

Multiple Choice

$$\frac{n^{-4}}{m^{-2}}$$

• $$\frac{m^2}{n^4}$$

• $$\frac{n^4}{m^2}$$

Multiple Choice

$$\frac{x^2y^{-3}}{5z^{-4}}$$

• $$\frac{x^2z^4}{5y^3}$$

• $$\frac{5z^4}{x^2y^3}$$

Multiple Choice

$$\left(\frac{r}{3s}\right)^{-3}$$

• $$\frac{r^3}{3s^3}$$

• $$\frac{9s^3}{r^3}$$

• $$\frac{27s^3}{r^3}$$

Quotient Rule

Multiple Choice

$$\frac{6^3}{6^4}$$

• $$6^1$$

• $$6^{-1}$$

Multiple Choice

$$\frac{t^4}{t^{-5}}$$

• $$t^9$$

• $$t^{-1}$$

Multiple Choice

$$\frac{\left(p+q\right)^{-3}}{\left(p+q\right)^{-7}},\ p\ne\ q$$

• $$\left(p+q\right)^{10}$$

• $$\left(p+q\right)^4$$

Multiple Choice

$$\frac{5^2xy^{-3}}{3^{-1}x^{-2}y^2}$$

• $$\frac{75x^3}{y^5}$$

• $$\frac{75y^5}{x^3}$$

Replace this text with your titleSimplify . Assume that all variables represent nonzero real numbers.

Multiple Choice

$$\frac{3^{15}}{\left(3^3\right)^4}$$

• 9
• 81
• 27
• 12

Multiple Choice

$$\left(4t\right)^5\left(4t\right)^{-3}$$

• 
  $$32t^2$$

• 
  $$64t^2$$

• 
  $$8t^2$$

• 
  $$16t^2$$

Multiple Choice

$$\left(\frac{7y^4}{10}\right)^{-3}$$

• 
  $$\frac{1000}{343y^{12}}$$

• 
  $$\frac{1000}{343y^6}$$

• 
  $$\frac{1000}{49y^{12}}$$

• 
  $$\frac{1000}{240y^4}$$

Multiple Choice

$$\frac{\left(a^2b^{-2}c\right)^{-3}}{\left(2ab^3c^{-4}\right)^5}$$

• $$\frac{a^{11}b^9c^{17}}{32}$$

• $$\frac{c^{17}}{32a^{11}b^9}$$

Multiple Choice

$$\frac{\ \left(5k\right)^{-6}\left(5k\right)^8}{\left(5k\right)^7\left(5k\right)^{-4}}$$

• 1

• -1

• $$\frac{1}{5k}$$

• $$5k$$

Multiple Choice

$$\frac{\left(2hj^2k^{-2}\cdot h^4j^{-1}k^4\right)^0}{2h^{-3}j^{-4}k^{-2}}$$

• 
  $$\frac{1}{2h^3j^4k^2}$$

• $$\frac{h^3j^4k^2}{2}$$