Question

Write each expression as a single power of 10.

Answer 1

Refer to below!

Step-by-step explanation (a):

`\rightarrow (10^(3) * 10^(4) )/(10^(5) ) \\\\\\ \rightarrow (10^(3 + 4) )/(10^(5) ) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \[[\text{Using exponent rule:} \ a^(2) * a^(4) = a^(4 + 2) = a^(6) ] \\\\\\ \rightarrow (10^(7) )/(10^(5) ) \\\\\\`

`\rightarrow 10^(7 - 5) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^(2) / a^(4) = a^(2 - 4) = a^(-2)] \\\\\rightarrow 10^(2)`

Step-by-step explanation (b):

`\rightarrow \huge{\text{(}{10^(4) * (10^(12) )/(10^(7) )\huge{\text{)}`

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

`\rightarrow \huge{\text{(}{10^(4) * {10^(5) }\huge{\text{)}`

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

`\rightarrow{10^(9) }`

Step-by-step explanation (c):

`\rightarrow \huge{\text{(}(10^(5) )/(10^(3) ) }\huge{\text{)}`

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

`\rightarrow 10^(2) }`

Step-by-step explanation (d):


`\rightarrow (10^(4) * 10^(5) * 10^(6) )/(10^(3) * 10^(7) )`


`\rightarrow (10^(4 + 5 + 6) )/(10^(3 + 7) ) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^(2) * a^(4) = a^(4 + 2) = a^(6) ]`


`\rightarrow (10^(15) )/(10^(10) )`


`\rightarrow 10^(15 - 10) } \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^(2) / a^(4) = a^(2 - 4) = a^(-2)]`


`\rightarrow 10^(5) }`

Step-by-step explanation (e):

`\rightarrow ((10^(5))^(2) )/((10^(2))^(3) )`

`\rightarrow (10^(5 * 2) )/(10^(2 * 3) ) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{Using exponent rule: }(a^(2) )^(5) = a^(2 * 5) = a^(10) ]`

`\rightarrow (10^(10) )/(10^(6) )`

`\rightarrow {10^(10 - 6) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{Using exponent rule:} \ a^(2) / a^(4) = a^(2 - 4) = a^(-2)]`

`\rightarrow {10^(4)`