Powers and roots

Properties of powers, scientific notation and radicals

The Powers and roots unit belongs to the Arithmetic and mental math section of Math Mental and has 16 lessons: properties of powers, scientific notation and radicals.

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Sample questions

In the lesson, numbers change every session and the solution appears after you answer.

$2^{5} \cdot 2^{-3}$
Step by step
1. $\displaystyle 2^{5 + (-3)} = 2^{2}$
Answer $4$
$\sqrt{72}$
Step by step
1. $\displaystyle \sqrt{72} = \sqrt{36 \cdot 2}$
2. $\displaystyle = \sqrt{36} \cdot \sqrt{2}$
Answer $6\sqrt{2}$
$18 - 3 \cdot (4 - 2^2) + 6 \div 2$
Step by step
1. $\displaystyle 4 - 2^2 = 0$
2. $\displaystyle 18 - 0 + 3$
Answer $21$

Lessons in this unit

Exponents 0 and 1 and powers of 10 Lesson, 8 questions
Negative base Lesson, 8 questions
Perfect squares Lesson, 8 questions
Larger square roots Lesson, 8 questions
Cube root Lesson, 8 questions
Product with the same base Lesson, 8 questions
Quotient with the same base Lesson, 8 questions
Power of a power Lesson, 8 questions
Practice: properties of powers Practice, 10 questions
Negative exponent Lesson, 8 questions
Scientific notation Lesson, 8 questions
Approximate root Lesson, 8 questions
Product and quotient of radicals Lesson, 8 questions
Simplifying radicals Lesson, 8 questions
Powers and roots in expressions Lesson, 8 questions
Unit test 12 questions

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Sample questions

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Lessons in this unit

Your first lesson takes five minutes