### Home > CCA2 > Chapter A > Lesson A.2.1 > ProblemA-56

A-56.

Simplify each expression. In parts (e) through (f) write the final answer in scientific notation.

1. $4^2 · 4^5$

If you wrote out all the factors of $4$, how many would you have? What shortcut can you use?

$4^7$

1. $(5^0)^3$

Multiply the exponents and simplify.

$1$

1. $x^{-5} · x^3$

Look at part (a) - use the exponent rule(s).

1. $(x^{-1} · y^2)^3$

Look at part (b) - use the exponent rule(s).

1. $(8 × 10^5) · (1.6 × 10^{-2})$

Use the Commutative and Associative properties of multiplication to rewrite the problem.

$(8 · 1.6) · (10^5 · 10^{-2})$

$1.28 · 10^4$

1. $\frac { 4 \times 10 ^ { 3 } } { 5 \times 10 ^ { 5 } }$

Rewrite the fraction using the Commutative and Associative properties.
Then simplify each fraction and convert to scientific notation.

$\frac{4}{5}\cdot \frac{10^{3}}{10^{5}}\ =\ 0.8\cdot 10^{-2}$

$8 · 10^{-3}$