options: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger.

Use square root and cube root symbols to represent solutions to equations of the form x^(2) = p and x^(3) = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that Ö2 is irrational.

Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^(2) × 3^(–5) = 3^(–3) = 1/3^(3) = 1/27.
problem_activity: Activity
In this practice activity, students prepare for the associated Algebra 1 lesson by practicing applying some of the properties they will need to use.
Student Facing
Evaluate:
\(\dfrac{3^5}{3^4}\)
\(\dfrac{3^1}{3^0}\)
\(\dfrac{3^{\text-1}}{3^{\text-2}}\)
\(\dfrac{3^{100}}{3^{99}}\)
\(\dfrac{3^{x+1}}{3^x}\)
Solve for
\(m\)
:
\(\dfrac{2^m}{2^7}=2\)
\(\dfrac{2^{100}}{2^m}=2\)
\(\dfrac{2^m}{2^x}=2\)
Write an equivalent expression using as few terms as possible:
\(3(x+1) + 4 - (3x + 4)\)
\(2(x+1) + 5 - (2x + 5)\)
\(2(x+2) + 5 - (2(x+1) + 5)\)
\(\text-5(x+1) + 3 - (\text-5x + 3)\)
\(\dfrac{5^{x+1}}{5^x}\)
\(\dfrac{7^{x+4}}{7^x}\)
Student Response
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Activity Synthesis
Either display the correct solutions or invite students check with another student to see if their answers are the same.  If there are any differences between solutions, invite students to ask questions or discuss whole group.


correct_option_index: 3