property of exponents: [tex] \sqrt{xy}= \sqrt{x} times \sqrt{y} [/tex] so
[tex] \sqrt[3]{6.4 times 10^{10}}= \sqrt[3]{6.4} times \sqrt[3]{10^10} [/tex]
exponents
3rd root of 10^10
property of expoentns
x^n times x^m=x^(n+m)
so
3rd root of x^3=x so
3rd root of 10^10=10^3 times [/tex] \sqrt[3]{10^10} [/tex]
then you have [tex] \sqrt[3]{6.4} times \sqrt[3]{10} times 10^{3} [/tex]
then multiply [tex] \sqrt[3]{6.4} times \sqrt[3]{10} [/tex] together and get [tex] \sqrt[3]{64} [/tex]
and we know thatn 64=4^3 so [tex] \sqrt[3]{64} [/tex]=4
so the answer is 10^3 times 4 or 4 times 1000 or 4000
the answer is 4000
another way to do it is multiply it out inside and get 64,000,000,000
then factor, 4000^3=64,000,000,000
then cube root
4000
the asnwer is 4000
