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

Explanation:

Step1: Isolate the term with the variable

Divide both sides of the equation (3(x + 9)^{\frac{3}{4}}=24) by (3): ((x + 9)^{\frac{3}{4}}=\frac{24}{3}=8)

Step2: Eliminate the exponent

Raise both sides of the equation ((x + 9)^{\frac{3}{4}} = 8) to the (\frac{4}{3}) power. Using the property ((a^{m})^{n}=a^{mn}), we have ((x + 9)^{\frac{3}{4}\times\frac{4}{3}}=8^{\frac{4}{3}}). Since (8 = 2^{3}), then (8^{\frac{4}{3}}=(2^{3})^{\frac{4}{3}}). By the power - of - a - power rule ((a^{m})^{n}=a^{mn}), ((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=7)

Answer:

C. 7