91Ó°ÊÓ

In Exercises \(5-48,\) simplify the given expressions. Express results with positive exponents only. $$\left(-t^{2}\right)^{7}$$

Solve the given problems. Refer to Appendix B for units of measurement and their symbols. For any positive or negative integer: (a) Is its absolute value always an integer? (b) Is its reciprocal always a rational number?

Evaluate each of the given expressions by performing the indicated operations. $$\frac{24}{3+(-5)}-4(-9) \div(-3)$$

Simplify the given expressions. In each of \(5-9\) and \(12-21,\) the result is an integer. $$\frac{7^{2} \sqrt{81}}{(-3)^{2} \sqrt{49}}$$

Perform the indicated multiplications. $$(x-2 y-4)(x-2 y+4)$$

Simplify the given algebraic expressions. $$-2[-x-2 a-(a-x)]$$

Set up an appropriate equation and solve. Data are accurate to two sig. digits unless greater accuracy is given. A car's radiator contains 12 L of antifreeze at a \(25 \%\) concentration. How many liters must be drained and then replaced by pure antifreeze to bring the concentration to \(50 \%\) (the manufacturer's "safe" level)?

Perform the indicated calculations using a calculator. All numbers are approximate. $$\left(3.642 \times 10^{-8}\right)\left(2.736 \times 10^{5}\right)$$

Assume that all numbers are approximate. (a) Estimate the result and (b) perform the indicated operations on a calculator and compare with the estimate. $$12.78+1.0495-1.633$$

Solve the given equations. $$|x|-1=8$$