Part 15

To multiply quantities having the same base, add exponents.

To divide quantities having the same base, subtract exponents.

To raise a quantity to a power, multiply exponents.

To extract a root, divide the exponent of the power by the index of the root.

1. Find the value of 3^2 - 5 x 4^0 + 8^(-2/3) + 1^(2/5).

2. Find the value of 8^(-2/3) + 9^(3/2) - 2^(-2) + 1^(-2/5) - 7^0.

Give the value of each of the following:

3. (3^0)/5, 3/(5^0), (3^0)/(5^0), 3^0 x 5, 3 x 5^0, 3^0 x 5^0, 3^0 + 5^0, 3^0 - 5^0.

4. Express 7^0 as some power of 7 divided by itself.

Simplify:

5. 16^(1/3) . 2^(1/2) . 32^(5/6). (Change to the same base first.)

6. [2/(8^(-3))]^(1/5).

7. [(x^n)^(n + 2)]/[(x^(n + 1))(x^(n - 1))].

8. (x + 3x^(2/3) - 2x^(1/3))(3 - 2x^(-1/3) + 4x^(-2/3)).

9. [(a^2b)/(c^2d)]^(1/2) x [(c^3d)/(ab^3)]^(1/3) x [(a^(1/3)c)/(b^(1/4)d^(5/12))]^2.

10. [(a^(-4))/(b^(-2)c)]^(-3/4) x [(a^(-1)b[c^(-3)]^(1/2))/(ab^(-1))]^(1/2).

11. [([a^2]^(1/3))/([b^(-1)]^(1/4)) . ([c^(-3)]^(1/2))/(a^(1/3)) . (b^(-1/4)a^(1/3))/(c^(-1))]^(-6).

~Reference:~ The chapter on Theory of Exponents in any algebra.

Solve for x:

1. x^(2/3) = 4.

2. x^(-3/4) = 8.

Factor:

3. x^(2/3) - 9.

4. x^(3/5) + 27.

5. x^(2a) - y^(-6).

6. a^(1/3) x^(1/2) - 3a^(1/3) + 5x^(1/2) - 15.

7. Find the H. C. F. and L. C. M. of a^2 + a^(3/2) b^(1/2) + a^(1/2) b^(3/2) - b^2, a^2 - a^(3/2) b^(1/2) - a^(1/2) b^(3/2) - b^2.

8. Simplify the product of: (ayx^(-1))^(1/2), (bxy^(-2))^(1/3), and (y^2a^(-2)b^(-2))^(1/4). (Princeton.)