### Home > CCA > Chapter 4 > Lesson 4.2.1 > Problem4-41

4-41.

Simplify each expression. In parts (c) and (d) write your answers using scientific notation.

1. $5^0·2^{−3}$

• Any number raised to the $0$ power is $1$.

$x^{-1}=\frac{1}{x}$

1. $\frac{a^3}{b^{-2}}\cdot\frac{ab^2}{a^4}$

• $ab^2$ is the same as $a^1b^2$.

• $b^4$

1. $2.3 \times 10 ^ { - 3 } \cdot 4.2 \times 10 ^ { 2 }$

• An equivalent expression is $(2.3\times4.2)\times(10^{−3}·10^2)$.

1. $( 3.5 \times 10 ^ { 3 } ) ^ { 2 }$

• An equivalent expression is $(3.5\times10^3)(3.5\times10^3)$.

• Unsimplified: $12.25\times10^6$