### Home > GB8I > Chapter 4 Unit 5 > Lesson INT1: 4.1.4 > Problem4-40

4-40.

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

1. $\quad 5 ^ { 0 } \cdot 2 ^ { - 3 }$

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

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

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

$ab^2$ is the same as $a^1b^2$.

$b^4$

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

• An equivalent expression is $(2.3 × 4.2) × (10^{−3} × 10^2)$.

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

• An equivalent expression is $(3.5 \times 10^3)(3.5 \times 10^3)$.

• Unsimplified: $12.25 \times 10^6$