Integer Exponents and Scientific Notation: example 10.70

Simplify: $(2 x^{−6} y^{8}) (−5 x^{5} y^{−3}) .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Simplify: $(3 u^{−5} v^{7}) (−4 u^{4} v^{−2}) .$

How did it go?

	$(2 x^{−6} y^{8}) (−5 x^{5} y^{−3})$
Rewrite with the like bases together.	$2 (−5) \cdot (x^{−6} x^{5}) \cdot (y^{8} y^{−3})$
Simplify.	$−10 \cdot x^{−1} \cdot y^{5}$
Use the definition of a negative exponent, $a^{- n} = \frac{1}{a^{n}} .$	$−10 \cdot \frac{1}{x^{1}} \cdot y^{5}$
Simplify.	$\frac{−10 y^{5}}{x}$

	$(2 x^{−6} y^{8}) (−5 x^{5} y^{−3})$
Rewrite with the like bases together.	$2 (−5) \cdot (x^{−6} x^{5}) \cdot (y^{8} y^{−3})$
Simplify.	$−10 \cdot x^{−1} \cdot y^{5}$
Use the definition of a negative exponent, $a^{- n} = \frac{1}{a^{n}} .$	$−10 \cdot \frac{1}{x^{1}} \cdot y^{5}$
Simplify.	$\frac{−10 y^{5}}{x}$