Exponents and Radicals

radicals

100

What is the solution to this problem? (36a⁵/4a⁴b⁵)^-2

(\frac{36a^5}{4a^4b^5})^{-2}

The solution would be 

\frac{b^{10}}{81a^2}

200

Is this true or false, any base powered by 0 exponent is one?

This is true 

300

Solve this, (a⁵)^-1

The answer is a^-5

400

When multiplying radicals you have to what?

1- Multiply any coefficients

2- Multiply the radicals

3- Keep the same root

500

What are the steps when adding and subtracting radicals.

1- Radicals can only be combined with addition/subtraction if they have the same radical

2- Simplify each radical separately

3- Combine the coefficients

4- Keep the same radical

exponents

100

Is this true or false, any non zero number with an exponent of zero is equivalent to 1?

True

200

when you multiply the coefficients do you add or multiply the exponents 

add the exponents 

300

Solve this 7(8¹)= 

The answer is 56.

400

Define exponent.

Number that tells you how many times your write your base and multiply.

500

Solve this 4a³b² (3a^-4b^-3)

The answer is 

\frac{12}{ab}

properties of exponents

100

a^{m *} aⁿ=?

a^m+n

200

(ab)ⁿ=?

aⁿ/bⁿ

300

a⁰=?

1

400

\frac{a^{-m}}{b^m} = ?

\frac{1}{a^mb^m}

500

Solve this 

\frac{21d^{18}e^5}{7d^{11}e^3}

The answer is 3d⁷e²

simplifying radicals

100

simplify: 

3\sqrt{8}

6\sqrt{2}

200

Rewrite with rational exponents:

root(3)((3x)^2)

(3x)^{\frac{2}{3}}

300

Simplify: 

\sqrt{75x^2y^5}

5xy^2\sqrt{3y}

400

simplify:

root(4)(16y^8)

2y²

500

Simplify: 

\sqrt{64m^3n^3}

8mn\sqrt{mn}

Operations with Radicals

100

3sqrt{8}+4sqrt{8}

7sqrt{8}

200

3sqrt{8}sqrt{8}

24

300

sqrt{2}(sqrt{3}+sqrt{4})

sqrt{6}+2sqrt{2}

400

3sqrt{8}-sqrt{32}

2sqrt{2}

500

3sqrt{2}(sqrt{5}-sqrt{20})

-3sqrt{10}