Unit 3 Exponents and Radicals

radicals

100

What must be true when adding and subtracting radicals.

1- The Radicals have the same radical form.

200

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

True

300

What base, raised to the 0 exponent, is not one?

Zero

400

What is the solution with a positive exponent; (a⁵)^-1

The answer is 1/a⁵

500

When multiplying radicals you have to what?

1- Multiply any coefficients

2- Multiply the radicals

3- Keep the same root

Positive exponents

100

Define exponent.

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

200

Solve this 7(8¹)= 

The answer is 56.

300

Solve this 

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

The answer is 3d⁷e²

400

What is the solution to this problem?

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

The solution would be 

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

500

Solve this;

 4a³b² (3a^-4b^-3)

The answer is 

\frac{12}{ab}

properties of exponents

100

a⁰=?

1

200

a^{m *} aⁿ=?

a^m+n

300

(ab)ⁿ=?

aⁿ/bⁿ

400

(a/b)^m=?

a^m/b^m

500

a^-n=?

1/aⁿ

simplifying radicals

100

sqrt(32)

4sqrt(2)

200

3sqrt(8)

6\sqrt{2}

300

simplify:

root(4)(16y^8)

2y²

400

Simplify: 

\sqrt{75x^2y^5}

5xy^2\sqrt{3y}

500

Simplify: 

\sqrt{64m^3n^3}

8mn\sqrt{mn}

Operations with Radicals

100

3sqrt{8}+4sqrt{8}

7sqrt{8}

200

3sqrt{8}-sqrt{32}

2sqrt{2}

300

3sqrt{8}sqrt{8}

24

400

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

sqrt{6}+2sqrt{2}

500

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

-3sqrt{10}

Back and Forth

100

Rewrite in Exponential form: 

root3(27)

27^{1/3}

200

Rewrite with rational exponents:

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

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

300

Rewrite in Radical Form: 

64^(2/3)

(root3(64))^2

400

Rewrite in Radical Form: 

(1/81)^(1/4)

root4(1/81)

500

Solve the following:

8^(2/3)

4