Question

Write each expression as a single power of 10.

Answer 1

Answer:

Refer to below!

Step-by-step explanation (a):

$\rightarrow \dfrac{10^{3} \times 10^{4} }{10^{5} } \\\\\\ \rightarrow \dfrac{10^{3 + 4} }{10^{5} } \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \[[\text{Using exponent rule:} \ a^{2} \times a^{4} = a^{4 + 2} = a^{6} ] \\\\\\ \rightarrow \dfrac{10^{7} }{10^{5} }$

$\rightarrow 10^{7 - 5} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \div a^{4} = a^{2 - 4} = a^{-2}] \\\\\rightarrow 10^{2}$

Step-by-step explanation (b):

$\rightarrow \huge{\text{(}{10^{4} \times \dfrac{10^{12} }{10^{7} }\huge{\text{)}$

$\rightarrow \huge{\text{(}{10^{4} \times {10^{12 - 7} }\huge{\text{)} \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \div a^{4} = a^{2 - 4} = a^{-2}]$

$\rightarrow \huge{\text{(}{10^{4} \times {10^{5} }\huge{\text{)}$

$\rightarrow \huge{\text{(}{10^{4 + 5} }\huge{\text{)}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \times a^{4} = a^{4 + 2} = a^{6} ]$

$\rightarrow{10^{9} }$

Step-by-step explanation (c):

$\rightarrow \huge{\text{(}\dfrac{10^{5} }{10^{3} } }\huge{\text{)}$

$\rightarrow \huge{\text{(}10^{5 - 3} }\huge{\text{)} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \div a^{4} = a^{2 - 4} = a^{-2}]$

$\rightarrow 10^{2} }$

Step-by-step explanation (d):

$\rightarrow \dfrac{10^{4} \times 10^{5} \times 10^{6} }{10^{3} \times 10^{7} }$

$\rightarrow \dfrac{10^{4 + 5 + 6} }{10^{3 + 7} } \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \times a^{4} = a^{4 + 2} = a^{6} ]$

$\rightarrow \dfrac{10^{15} }{10^{10} }$

$\rightarrow 10^{15 - 10} } \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \div a^{4} = a^{2 - 4} = a^{-2}]$

$\rightarrow 10^{5} }$

Step-by-step explanation (e):

$\rightarrow \dfrac{(10^{5})^{2} }{(10^{2})^{3} }$

$\rightarrow \dfrac{10^{5 \times 2} }{10^{2 \times 3} } \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{Using exponent rule: }(a^{2} )^{5} = a^{2 \times 5} = a^{10} ]$

$\rightarrow \dfrac{10^{10} }{10^{6} }$

$\rightarrow {10^{10 - 6} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{Using exponent rule:} \ a^{2} \div a^{4} = a^{2 - 4} = a^{-2}]$

$\rightarrow {10^{4}$