22 (a) Solve the equation x^(3/2) = 8. The following is the graph of y = −x2 + 12x − 11

Question

ScanSolve AI Tutor · Accepted Answer

Alright, Chimuka, let's solve this equation.

22 (a) Solve the equation $x^{\frac{3}{2}} = 8$ .

To solve for $x$ , raise both sides of the equation to the power of $\frac{2}{3}$ .
This is the reciprocal of the exponent $\frac{3}{2}$ .
$\left(x^{\frac{3}{2}}\right)^{\frac{2}{3}} = 8^{\frac{2}{3}}$
Simplify the left side using the power rule $(a^m)^n = a^{mn}$ .
$x^{\frac{3}{2} \times \frac{2}{3}} = 8^{\frac{2}{3}}$ $x^1 = 8^{\frac{2}{3}}$ $x = 8^{\frac{2}{3}}$
Evaluate $8^{\frac{2}{3}}$ .
This can be written as $(\sqrt[3]{8})^2$ .
First, find the cube root of 8.
$\sqrt[3]{8} = 2$
Square the result from Step 3.
$x = (2)^2$ $x = 4$
The solution to the equation is $\boxed{x=4}$ .

22 (a) Solve the equation x^(3/2) = 8. The following is the graph of y = -x2 + 12x - 11