Algebra 1B Properties of Exponents Review

Multiplying Monomials

100

Write the product using exponents$\colon$ $q \cdot q \cdot q \cdot q \cdot q \cdot q$

$q^{6}$

200

Write the product using exponents$\colon$ $t^{5}\cdot t^{5}$

t^{10}

300

Simplify$\colon (-2k^{3})\cdot(-2k^{4})\cdot(-2k^{6})$

$ -8k^{13}$

400

Simplify$\colon (7s^{4}t^{4})\cdot(5s^{2}t)$

$35s^{6}t^{5}$

500

An amount of bacteria DOUBLES in size every HALF HOUR. If there was $2,000$ bacteria at $12\colon 00$PM, how much bacteria grew exponentially at $3\colon 00$PM ?

$2,000\cdot (2)^{6} = 128,000$ bacteria

Dividing Monomials

100

Simplify and Evaluate $\colon \left(\frac{6^{11}}{6^{8}}\right)$

$6^{3} = 216$

200

Simplify $\colon \left(\frac{y^{5}}{z^{9}}\right)^{6}$

$\frac{y^{30}}{z^{54}}$

300

Simplify$\colon \frac{24x^{6}y^{4}}{-4x^{5}y} $

$-6xy^{3} $

400

Simplify the expression $\colon \left(\frac{3a^{3}b^{4}}{5a^{2}b^{3}}\right)^{2}$

$\frac{9a^{2}b^{2}}{25}$

500

Simplify $\colon \frac{12(x^{3}y)^{7}}{(2xy^{5})^{2}}$

$\frac{3x^{19}}{y^{3}}$

Raising Powers to a Power

100

Simplify$\colon \left ( \frac{3}{x} \right )^{2}$

$\left ( \frac{9}{x^{2}} \right )$

200

Simplify$\colon (-v^{4})^{6}$

$v^{24}$

300

Simplify$\colon 9(5g^{4})^{3}$

$1125g^{12}$

400

Evaluate$ ( ka)^{e}$ for $k = 4, a = 5, e = 2$

$(4\cdot 5)^{2} = 4^{2}\cdot 5^{2} = 400$

500

Simplify$\colon (3x^{3}y^{3})^{2}\cdot (-3x^{4}y^{2})^{2}$

$81x^{14}y^{10}$

Negative and Zero Exponents

100

Evaluate the expression $\colon 2^{-5}\cdot 2^{0}$

$\frac{1}{32}$

200

Simplify and write the expression with positive exponents only $\colon 3x^{-1}y^{0}$

$\frac{3}{x}$

300

Simplify the expression with positive exponents only $\colon \frac{x^{-4}}{x^{-9}}$

$x^{5}$

400

Simplify the expression using positive exponents only $\colon \frac{2a^{4}b^{-2}}{4a^{-3}b^{-8}}$

$\frac{a^{7}b^{6}}{2}$

500

Simplify the expression using positive exponents only $\colon\frac{28a^{4}b^{5}c^{-7}}{4a^{0}b^{-3}c^{3}}$

$\frac{7a^4b^8}{c^{10}}$

Scientific and Decimal Notation

100

What is the value of $10^{8}$?

100,000,000.

200

What is the value of $(1\times 10^{2})^{3}$?

$(1\times 10^{6}) = 1,000,000$

300

Write this number in scientific notation $\colon 0.00000580$

$5.80\times 10^{-6}$

400

Simplify the expression using scientific notation $\colon\frac{24\times 10^{2}}{6\times 10^{9}}$

$4\times 10^{-7}$

500

Convert the number from Scientific Notation to a Decimal Notation $ 5.5\times 10^{-9}$

$0.0000000055$