Answer:
7
Step-by-step explanation:
[tex] \frac{ {7}^{8} \times {7}^{3} \times {7}^{4} }{ {7}^{9} \times {7}^{5} } [/tex]
Step 1 : simplify denominator and numerator.
To do this we must multiply the numbers on top as well as the numbers on the bottom.
Multiplying exponents with the same base rule:
[tex] {a}^{b} \times {a}^{c} = {a}^{b + c} [/tex]
so when multiplying exponents with the same base we simply keep the base the same and add the exponents
using this rule we can simplify the denominator and numerator
Denominator :
[tex] {7}^{8} \times {7}^{3} \times {7}^{4} [/tex]
keep the base the same and add the exponents
[tex] {7}^{8} \times {7}^{3} \times {7}^{4} = {7}^{8 + 3 + 4} = {7}^{15} [/tex]
Numerator:
[tex] {7}^{9} \times {7}^{5} [/tex]
keep the base the same and add the exponents
[tex] {7}^{9} \times {7}^{5} = {7}^{9 + 5} = {7}^{14} [/tex]
We now have
[tex] \frac{ {7}^{15} }{ {7}^{14} } [/tex]
Next we must divide the exponents.
Dividing exponent rule ( with same base )
[tex] \frac{ {a}^{b} }{ {a}^{c} } = {a}^{b - c} [/tex]
So when dividing exponents with the same base we simply keep the base the same and subtract the exponent of the denominator by the exponent of the numerator
Applying this we get
[tex] \frac{ {7}^{15} }{ {7}^{14} } = {7}^{15 - 14} = {7}^{1} = 7[/tex]
And we are done!
