91Ó°ÊÓ

Simplify by writing each expression wth positive exponents. Assume that all variables represent nonzero real numbers. $$ \frac{\left(9^{-1} z^{-2} x\right)^{-1}\left(4 z^{2} x^{4}\right)^{-2}}{\left(5 z^{-2} x^{-3}\right)^{2}} $$

Simplify by writing each expression wth positive exponents. Assume that all variables represent nonzero real numbers. $$ \frac{\left(4^{-1} a^{-1} b^{-2}\right)^{-2}\left(5 a^{-3} b^{4}\right)^{-2}}{\left(3 a^{-3} b^{-5}\right)^{2}} $$

Explain why \(\left(3 x^{2} y^{3}\right)^{4}\) is not equivalent to \((3 \cdot 4) x^{8} y^{12}\)

Use scientific notation to calculate the answer to each problem. See Examples 3-5. Venus is \(6.68 \times 10^{7} \mathrm{mi}\) from the sun. If light travels at a speed of \(1.86 \times 10^{5} \mathrm{mi}\) per sec, how long does it take light to travel from the sun to Venus? (Source: World Almanac and Book of Facts.)

Write each product as a sum of terms. Write answers with positive exponents only. Simplify each term. $$ \frac{1}{2 p}\left(4 p^{2}+2 p+8\right) $$

Write each product as a sum of terms. Write answers with positive exponents only. Simplify each term. $$ \frac{1}{5 x}\left(5 x^{2}-10 x+45\right) $$

Perform each indicated operation. Find the difference between the sum of \(5 x^{2}+2 x-3\) and \(x^{2}-8 x+2\) and the sum of \(7 x^{2}-3 x+6\) and \(-x^{2}+4 x-6\)

Use scientific notation to calculate the answer to each problem. See Examples 3-5. During the \(2007-2008\) season, Broadway shows grossed a total of \(9.38 \times 10^{8}\) dollars. Total attendance for the season was \(1.23 \times 10^{7} .\) What was the average ticket price for a Broadway show? (Source: The Broadway League.)

Write each product as a sum of terms. Write answers with positive exponents only. Simplify each term. $$ \frac{1}{3 m}\left(m^{3}+9 m^{2}-6 m\right) $$

Find each product. In Exercises \(81-84,89,\) and \(90,\) apply the meaning of exponents. $$ 7(4 m-3)(2 m+1) $$