Answers:
[tex]y^2(y^4) = \boldsymbol{y^6}\\\\(2y)^2 = \boldsymbol{4y^2}\\\\(y/4)^2 = \boldsymbol{y^2/16}\\\\2(y^3)^3 = \boldsymbol{2y^9}\\\\[/tex]
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Explanation:
For the first expression, we use the rule that [tex]a^b*a^c = a^{b+c}[/tex]. We add the exponents when multiplying exponentials of the same base. So, [tex]y^2*y^4 = y^{2+4} = \boldsymbol{y^6}[/tex]
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In the second expression, we can expand out [tex](2y)^2[/tex] into [tex](2y)*(2y)[/tex]. The coefficients 2 and 2 multiply to 2*2 = 4 as the final coefficient. The y terms multiply to [tex]y*y = y^2[/tex]. So overall, that's how [tex](2y)^2 = \boldsymbol{4y^2}[/tex]
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We use the same idea for the third expression. We'll have two copies of y/4 multiplied together to end up with [tex]\boldsymbol{y^2/16}[/tex]. We have [tex]y^2[/tex] in the numerator and 16 in the denominator.
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For the fourth expression, we can use the rule that [tex](a^b)^c = a^{b*c}[/tex]. In other words, if we raised [tex]a^b[/tex] to some other exponent c, then it's the same as writing [tex]a^{b*c}[/tex]. We multiply the exponents.
The exponents in this case are 3 and 3 which multiply to 9. The 2 is then tacked up front to get [tex]\boldsymbol{2y^9}[/tex]
