Raising a Product or a Quotient to a power. Simplify. Assume that no denominator is 0

W2 College Algebra I

#84.) Raising a Product or a Quotient to a power. Simplify. Assume that no denominator is 0 and that 0^0 is not considered.

( X^5/-3y^3)^4

#36.) Expressions of the Form √a^2 Simplify. Variables may represent any real number, so remember to use absolute – value notation when necessary. If a root cannot be simplified, state this.

√ 16t^2

1.) Identify the base and the exponent.

6x^3

The base is _______.

2.) Multiply and simplify. Type answer as one base to a nonnegative power.

S^4 * S^5 =

3.) Simplify.

( a^4b^8) (a^6b^7) =

4.) Simplify. Assume that no denominator is 0.

S^11 ∕ s =

5.) Divide and simplify.

4b^8 ∕ 2b^4 =

6.) Simplify. Assume that no denominator is 0.

p^8q^8 ∕ p^0q^4 =

7.) Simplify.

8^0 + 4^0 =

8.) Simplify. Simplify answer, use positive exponents only.

(x^6)^4

9.) Simplify answer, use positive exponents only.

(4x^4)^2 (3x^6) =

10.) Simplify. Simplify answer, use positive exponents only.

(f^8 ∕ g^9) ^7 =

11.) Express using a positive exponent. Simplify answer. Type positive exponent.

R ^-7

12.) Express using positive exponents and if possible, simplify. Simplify answer, type exponential notation with positive exponents.

Z^-4 / 8x^6 =

13.) First use the product rule to multiply the terms and then rewrite the expression using positive exponents. Simplify answer, use positive exponents only.

C^-8 * C^-5

14.) Multiply and simplify. Give answers using positive exponents. Simplify answer, type exponential notation with positive exponents.

(7p^-10 n^18) * (-6p^-4 n^-2)

15.) Simplify. Do not use negative exponents in the answer. Use integers or fractions for any numbers in the expression. Simplify answer.

-4a^-2 / 8b^-4 =

16.) Simplify. Do not use negative exponents in the answer. Simplify answer, use integers or fractions for any numbers in the expression, use positive exponents only.

-9p^2q^-3

-3p^4q^-7

17.) Express the following number in decimal notation.

2.68 x 10^-5 =

18.) Express the following number in scientific notation.

6,500,000

19.) Find each function value, if it exists. Simplify answer, use radicals as needed.

F(t)= √ t^2 + 1

20.) Simplify. Remember to use absolute – value notation when necessary. If a root cannot be simplified, state this. Simplify answer.

√ (-8c)^2

21.) Find the square root that is a real number.

√ - 25

22.) Simplify the following.

3√ -27

23.) Rewrite without exponents. Simplify answer, type exact answer, using radicals as needed.

X ^1/3

24.) Use radical notation to rewrite the expression. Simplify, if possible. Rewrite the expression using radical notation.

(xy)^1/11 =

25.) Multiply. Type exact answer, using radicals as needed.

4√ 3 * 4√ 5

26.) Multiply. Type exact answer using radicals as needed.

√ 7a * √ 6b

27). Express in terms of i. Simplify answer, type answer in the form a + bi.

√ -10

28.) Subtract and simplify. Simplify answer, type answer in the form a + bi.

(7 – I ) – (9 + 5i)

29.) Multiply. Simplify answer, type your answer in the form a + bi.

-7i * 2i =

30.) Multiply. Simplify answer, type answer in the form a + bi . Type exact answer, using radicals as needed.

√-49 * √-81 =