Whale-and-Flea WandaPowerhouse · exponents and exponential functions

A whale balloon and a flea on her hat: negative exponents and scientific notation.

Integer Exponents and Scientific Notation

Negative exponents and scientific notation. In MathBound, the free Algebra I adventure game, Whale-and-Flea Wanda asks these problems, and the only way past is to solve them.

Part of Exponents and Exponential Functions: chapter 7 of the standard course.

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10 questions, no sign-up, nothing saved. Climbs from the basics to harder questions.

What you will practice

Negative Exponents. Rewrite an expression with a negative exponent using the definition a^-n = 1/a^n.
Simplify Integer Exponents. Simplify expressions involving negative exponents using the Product or Quotient properties.
Scientific Notation Conversions. Convert a large number from standard decimal form to scientific notation and vice versa.
Scientific Notation Operations. Multiply or divide two numbers written in scientific notation without converting to standard form first.

Worked examples

Made by the game’s own question engine. Try each one, then open its steps.

Example 1 · Negative Exponents

Simplify:

3^{- 2}

$- 9$
$9$
$\frac{1}{9}$
$\frac{1}{6}$

Show the worked steps

$A$ $negative$ $exponent$ $means$ $a$ $reciprocal,$ $not$ $a$ $negative$ $number.$
$3^{- 2} = \frac{1}{3 ^{2}} = \frac{1}{9} .$

Answer: $\frac{1}{9}$

Example 2 · Simplify Integer Exponents

Simplify:

\frac{p ^{- 3}}{p ^{3}}

$1$
$p^{6}$
$\frac{1}{p}$
$\frac{1}{p ^{6}}$

Show the worked steps

$Subtract$ $the$ $exponents:$ $- 3 - 3 = - 6 .$
$A$ $negative$ $result$ $becomes$ $a$ $reciprocal.$ $\frac{1}{p ^{6}} .$

Answer: $\frac{1}{p ^{6}}$

Example 3 · Scientific Notation Conversions

Write

2.39 \cdot 1 0^{8}

in

standard

form.

$239, 000, 000$
$191.2$
$2, 390, 000, 000$
$23, 900, 000$

Show the worked steps

$1 0^{8}$ $moves$ $the$ $decimal$ $point$ $8$ $places$ $to$ $the$ $right.$
$2.39 \cdot 1 0^{8} = 239, 000, 000 .$

Answer: $239, 000, 000$

Where it is in your textbook

Textbook	Lessons
Standard course	7.2
Big Ideas Math Algebra 1	6.1
Big Ideas Math Algebra 1 (2022)	6.1
CPM Core Connections Algebra	3.1.2, 7.2.2
CPS Skyline Algebra	2.4-2.5
Glencoe Algebra 1	7-2, 7-4
Holt McDougal Larson Algebra 1	7.3
Illustrative Mathematics Algebra 1	5.6-5.7
Illustrative Mathematics Algebra 1 (v.360)	6.6-6.7
Math Nation Algebra 1 (Florida B.E.S.T.)	1.4, 2.2, 2.3
MVP Mathematics I (Integrated Math 1)	2.5
Open Up NC Math 1 (MVP)	2.4, 2.5
OpenStax Elementary Algebra 2e	6.7
Pearson Algebra 1 Common Core	7-1, 7-2, 7-4
Reveal Algebra 1	8-1, 8-3
SpringBoard Algebra 1	19

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