Evaluate fourth root of 9 multiplied by square root of 9 over the fourth root of 9 to the power of 5.

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Evaluate fourth root of 9 multiplied by square root of 9 over the fourth root of 9 to the power of 5.

Mathematics
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9 to the power of negative 1 over 2 9 to the power of negative 1 over 4 9 92
If I understand correctly, the question is to simplify\[\frac{ 9^{\frac{ 1 }{ 4 }} \times 9^{\frac{ 1 }{ 2 }} }{ \left( 9^{\frac{ 1 }{ 4 }} \right)^{5} }\]Is this correct?
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OK. When working with exponents, many times it is easier to express them as fractions rather than radicals. My statement is equivalent to yours. Do you understand the fractional exponents?
yes a lil
For example,\[\sqrt{x}=x ^{\frac{ 1 }{ 2 }}\]\[\sqrt[3]{x}=x ^{\frac{ 1 }{ 3 }}\]\[\sqrt[4]{x}=x ^{\frac{ 1 }{ 4 }}\]\[\sqrt[4]{x ^{5}}=\left( x ^{5} \right)^{\frac{ 1 }{ 4 }}=x ^{\frac{ 5 }{ 4 }}\]
So, with the expression written with fractional exponents, simplify the numerator first. The rule when multiplying powers with the same base is to ADD the exponents. Then, divide the numerator by the denominator, The rule when dividing powers with the same base is that you SUBTRACT the exponents. This help?
it does a lil bit what would the answer be?
For example,\[\frac{ 3^{\frac{ 1 }{ 4 }}\times 3^{\frac{ 1 }{ 2 }} }{ 3^{\frac{ 7 }{ 4 }} }=\frac{ 3^{\frac{ 3 }{ 4 }} }{ 3^{\frac{ 7 }{ 4 }} }=3^\left( \frac{ 3 }{ 4 } -\frac{ 7 }{ 4 }\right)=3^{-\frac{ 4 }{ 4 }}=3^{-1}\]
Sorry for taking so long with the typing. I can't give you the answer, but I can check yours. What do you get?
it ok and i got B? is that correct
Don't think so. Let's take it one step at a time. What do you get when you simplify just the numerator?
9
\[9^{\frac{ 1 }{ 4 }}\times 9^{\frac{ 1 }{ 2 }} = 9^{\left( \frac{ 1 }{ 4 } +\frac{ 1 }{ 2 }\right)}=?\]
is it C?
Don't think so. How about simplifying the numerator first, as above. What would you get?
What is 1/4 + 1/2 ?
3/4
Hello? Do you still want my help?
3/4
Right on! So the numerator simplifies to\[9^{\frac{ 3 }{ 4 }}\]Now simplify the denominator. It is a power raise to another exponent. The rule in this case is to MULTIPLY the exponents. So\[\left(9^{\frac{ 1 }{ 4 }} \right)^{5}=9^{?}\] What do you get?
2?
No. Keep the base (9) and multiply just the exponents together.\[\left( 9^{\frac{ 1 }{ 4 }} \right)^{5} = 9^{\left( \frac{ 1 }{ 4 } \times5\right)} = 9^{?}\]
In other words, what is 1/4 x 5 ?
5/4?
Perfect. Now your problem has been simplified to \[\frac{ 9^{\frac{ 3 }{ 4 }} }{ 9^{\frac{ 5 }{ 4 }} }\]When dividing powers with the same base, the rule is to keep the base and SUBTRACT the exponents. Therefore\[\frac{ 9^{\frac{ 3 }{ 4 }} }{ 9^{\frac{ 5 }{ 4 }} } = 9^{\left( \frac{ 3 }{ 4 } -\frac{ 5 }{ 4 }\right)} = 9^{?}\]
In other words, what is 3/4 - 5/4 ?
-1/2
Terrific. That's your answer.\[9^{-\frac{ 1 }{ 2 }}\] Lot of small step. And lots of rules for working with exponents. Well done!
thank you very much
You're welcome. A bit of practice, and you'll be a master.

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