91Ó°ÊÓ

Use scientific notation to calculate the answer to each problem. Write answers in scientific notation. $$ \frac{0.0000016(240,000,000)}{0.00002(0.0032)} $$

The special product $$ (x+y)(x-y)=x^{2}-y^{2} $$ $$ \text { can be used to perform some multiplication problems. Here are two examples.} $$ $$ \begin{aligned} 51 \times 49 &=(50+1)(50-1) \\ &=50^{2}-1^{2} \\ &=2500-1^{2} \\ &=2499 \end{aligned} \quad | \begin{aligned} 102 \times 98 &=(100+2)(100-2) \\ &=100^{2}-2^{2} \\ &=10,000-4 \\ &=9996 \end{aligned} $$ Once these patterns are recognized, multiplications of this type can be done mentally. Use this method to calculate each product mentally. $$ 201 \times 199 $$

Add or subtract as indicated. $$ (-5 t+13 s)+(8 t-3 s) $$

The special product $$ (x+y)(x-y)=x^{2}-y^{2} $$ $$ \text { can be used to perform some multiplication problems. Here are two examples.} $$ $$ \begin{aligned} 51 \times 49 &=(50+1)(50-1) \\ &=50^{2}-1^{2} \\ &=2500-1^{2} \\ &=2499 \end{aligned} \quad | \begin{aligned} 102 \times 98 &=(100+2)(100-2) \\ &=100^{2}-2^{2} \\ &=10,000-4 \\ &=9996 \end{aligned} $$ Once these patterns are recognized, multiplications of this type can be done mentally. Use this method to calculate each product mentally. $$ 301 \times 299 $$

Use scientific notation to calculate the answer to each problem. Write answers in scientific notation. $$ \frac{0.000015(42,000,000)}{0.00009(0.000005)} $$

Simplify by writing each expression with positive exponents. Assume that all variables represent nonzero real numbers. See Example \(5 .\) $$ \frac{\left(m^{8} n^{-4}\right)^{2}}{m^{-2} n^{5}} $$

Add or subtract as indicated. $$ (4 x+2 x y-3)-(-2 x+3 x y+4) $$

Perform each division. $$ \frac{x^{4}-4 x^{3}+5 x^{2}-3 x+2}{x^{2}+3} $$

The special product $$ (x+y)(x-y)=x^{2}-y^{2} $$ $$ \text { can be used to perform some multiplication problems. Here are two examples.} $$ $$ \begin{aligned} 51 \times 49 &=(50+1)(50-1) \\ &=50^{2}-1^{2} \\ &=2500-1^{2} \\ &=2499 \end{aligned} \quad | \begin{aligned} 102 \times 98 &=(100+2)(100-2) \\ &=100^{2}-2^{2} \\ &=10,000-4 \\ &=9996 \end{aligned} $$ Once these patterns are recognized, multiplications of this type can be done mentally. Use this method to calculate each product mentally. $$ 20 \frac{1}{2} \times 19 \frac{1}{2} $$

Perform each division. $$ \frac{3 t^{4}+5 t^{3}-8 t^{2}-13 t+2}{t^{2}-5} $$