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question 10
which of the following is equal to ( 70y^{3/4} - 21y^{11/4} )?
○ nothing in this list is correct.
○ ( 7y^{1/4}(10y^3 - 3y^{11}) )
○ ( 49y^{3/11} )
○ ( 7y^{3/4}(10 - 3y^2) )

Explanation:

Step1: Find the GCF of coefficients and variables

The greatest common factor (GCF) of 70 and 21 is 7. For the variable part \(y^{3/4}\) and \(y^{11/4}\), the GCF is \(y^{3/4}\) (since we take the lower exponent when factoring out).

Step2: Factor out the GCF

Factor out \(7y^{3/4}\) from \(70y^{3/4}-21y^{11/4}\).
First, divide \(70y^{3/4}\) by \(7y^{3/4}\): \(\frac{70y^{3/4}}{7y^{3/4}} = 10\).
Then, divide \(-21y^{11/4}\) by \(7y^{3/4}\): \(\frac{-21y^{11/4}}{7y^{3/4}}=- 3y^{\frac{11}{4}-\frac{3}{4}}=-3y^{2}\) (using the rule \(a^m\div a^n=a^{m - n}\)).
So, \(70y^{3/4}-21y^{11/4}=7y^{3/4}(10 - 3y^{2})\).

Answer:

\(7y^{3/4}(10 - 3y^{2})\) (the option corresponding to this expression)