Factors of 4

[Sissy Devane]

Multiply and simplify by factoring
?10,000 × ?10,000,000
Here is what I did,
I factored ?10,000 as ?(625•16)
I factored ?10,000,000 as ?(625•625•16•16)
So I have:
?625 • ?16 • ?625 • ?625 • ?16 • ?16
Then I simplified each fourth root:
5 • 4 • 5 • 5 • 4 • 4 = 8,000
Is this the proper way to do this problem? Is my answer correct?

 

[Denis]

I factored ?10,000,000 as ?(625•625•16•16)

?(625•625•16•16) = 100,000,000

 

[Mrspi]

Multiply and simplify by factoring
?10,000 × ?10,000,000
Here is what I did,
I factored ?10,000 as ?(625•16)
I factored ?10,000,000 as ?(625•625•16•16)
So I have:
?625 • ?16 • ?625 • ?625 • ?16 • ?16
Then I simplified each fourth root:
5 • 4 • 5 • 5 • 4 • 4 = 8,000
Is this the proper way to do this problem? Is my answer correct?

10,000 is 10[sup:q275w5lt]4[/sup:q275w5lt]
10,000,000 is 10[sup:q275w5lt]7[/sup:q275w5lt]

so, ?10,000 * ?10,000,000 = ?10[sup:q275w5lt]4[/sup:q275w5lt] * ?10[sup:q275w5lt]7[/sup:q275w5lt]
or,
10 * ?(10[sup:q275w5lt]4[/sup:q275w5lt] * 10[sup:q275w5lt]3[/sup:q275w5lt])
or,
10 * ?10[sup:q275w5lt]4[/sup:q275w5lt] * ?10[sup:q275w5lt]3[/sup:q275w5lt]

or,
10*10 * ?10[sup:q275w5lt]3[/sup:q275w5lt]

100 * ?10[sup:q275w5lt]3[/sup:q275w5lt]

 

[soroban]

Hello, Sissy!

Are those fourth roots?

Multiply and simplify by factoring : .\(\displaystyle \sqrt[4]{10,000} \times \sqrt[4]{10,000,000}\)

\(\displaystyle \text{We have: }\;\sqrt[4]{10^4}\times \sqrt[4]{10^7} \;=\;\sqrt[4]{10^4\times 10^7} \;=\;\sqrt[4]{10^{11}}\)

. . . . . . \(\displaystyle = \;\sqrt[4]{10^8\times 10^3} \;=\;\sqrt[4]{10^8}\times \sqrt[4]{10^3} \;=\; \;=\;10^2\times\sqrt[4]{10^3} \;=\;100\sqrt[4]{1000}\)