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

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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 =