Answer
a. $10^{5} = 1000000$
b. $10^{6} = 10000000$
Work Step by Step
a. $10^{9}$ x $10^{-4}$
Recall the product rule: $a^{m}⋅a^{n}=a^{m+n}$
Hence,
$$10^{9} \cdot 10^{-4} = 10^{9+(-4)}$$ $$=10^{5}$$
To evaluate the expression, move the decimal point $5$ places to the right since the exponent is positive. Thus,
$$10^{5} = 1000000$$
b. $\frac{10^{4}}{10^{-2}}$
Recall the quotient rule: $\frac{a^{m}}{a^{n}}=a^{m-n}$ and $\frac{a^{n}}{a^{m}}=\frac{1}{a^{m+n}}$ if $m>n$
Hence,
$$\frac{10^{4}}{10^{-2}} = \frac{10^{4}}{10^{-2}}$$ $$=10^{4-(-2)}$$ $$=10^{6}$$
To evaluate the expression, move the decimal point $6$ places to the right since the exponent is positive. Thus,
$$10^{6} = 10000000$$
