select the correct answer.\nwhat is the solution to the equation?\n$3(x + 9)^{\frac{3}{4}} = 24$\na. -3\nb…

Explanation:

Step1: Divide both sides by 3

To isolate the term with the exponent, we divide both sides of the equation ( 3(x + 9)^{\frac{3}{4}} = 24 ) by 3. ( \frac{3(x + 9)^{\frac{3}{4}}}{3} = \frac{24}{3} ) Simplifying, we get ( (x + 9)^{\frac{3}{4}} = 8 )

Step2: Raise both sides to the power of ( \frac{4}{3} )

To eliminate the exponent ( \frac{3}{4} ), we raise both sides to the power of ( \frac{4}{3} ). Recall that ( (a^m)^n = a^{mn} ), so ( \left( (x + 9)^{\frac{3}{4}} \right)^{\frac{4}{3}} = (x + 9)^{\frac{3}{4} \times \frac{4}{3}} = x + 9 ). ( \left( (x + 9)^{\frac{3}{4}} \right)^{\frac{4}{3}} = 8^{\frac{4}{3}} ) First, we can rewrite 8 as ( 2^3 ), so ( 8^{\frac{4}{3}} = (2^3)^{\frac{4}{3}} ). Using the power - of - a - power rule ( (a^m)^n=a^{mn} ), we have ( (2^3)^{\frac{4}{3}}=2^{3\times\frac{4}{3}} = 2^4=16 ). So ( x + 9=16 )

Step3: Solve for x

Subtract 9 from both sides of the equation ( x + 9 = 16 ) ( x=16 - 9 ) ( x = 7 )

Answer:

C. 7