Question

Cube root (6.4 * 10^10)

Answer 1

property of exponents:
`√(xy)= √(x) times √(y)` so

`\sqrt[3]{6.4 times 10^(10)}= \sqrt[3]{6.4} times \sqrt[3]{10^10}`
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
`\sqrt[3]{6.4} times \sqrt[3]{10} times 10^(3)`
then multiply
`\sqrt[3]{6.4} times \sqrt[3]{10}` together and get
`\sqrt[3]{64}`
and we know thatn 64=4^3 so
`\sqrt[3]{64}`=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