1.
Simplify \( \frac{4xy}{35} \div \frac{16x}{7y^2} \).
2.
Simplify \( (4^{x+2})(4^x) \).
3.
Simplify \( (u^3)^2 \).
4.
Give the quotient of this expression in simplest form: \( \frac{4a^6}{3b} \div \frac{2a^2}{9b^2} \).
5.
Simplify \( \frac{(10m^3)^4(0.1m^2)^4}{(100m^2)(0.01m)^2} \).
6.
Simplify for all permissible values: \( \left(\frac{24y^2z^3}{30x}\right)\left(\frac{35x^3}{18y^3z^4}\right) \).
7.
Which expression is equal to \( \frac{64}{27} \)?
8.
Simplify: \( \frac{8t}{21s} \times \frac{3s}{4} \).
9.
Evaluate \( \frac{(3^2)(3^{-3})}{3} \).
10.
A colony of Fruit Flies triples every 30 minutes. If there are 19,683 Fruit Flies now, how many were present 2 hours ago?
11.
Determine the value of \(n\) that makes \( \left(\frac{5}{4}\right)^n=\frac{64}{125} \).
12.
Simplify \( \left(\frac{5}{2}a^{-4}b^{7}\right)^{-3} \).
13.
Eighteen cement squares cover a patio with an area of 40.5 m². What is the side length of one square?
14.
Simplify \( (a^{3}b^{2})(ab^{-4}) \).
15.
The remaining mass of radioactive iodine-131 is given by \(M=M_0(2)^{-t/8}\). If the initial amount is 726 grams, how much is left after 8 days?
16.
Evaluate \(3^{-2}\) without using a calculator.
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