7. If \( m^{\frac{3}{2}}=8 \), what is the value of \( m \) ? (A) 2 (B) 4 (C) 6 (D) 10 (E) \( 16 \sqrt{2} \)

Given the equation \[ m^{\frac{3}{2}} = 8 \] **Step 1:** Isolate \( m \) by raising both sides of the equation to the power of \( \frac{2}{3} \). This gives: \[ \left(m^{\frac{3}{2}}\right)^{\frac{2}{3}} = 8^{\frac{2}{3}} \] **Step 2:** Simplify the left-hand side using the power rule \((a^b)^c = a^{b \cdot c}\): \[ m^{\left(\frac{3}{2} \cdot \frac{2}{3}\right)} = m^1 = m \] Thus, \[ m = 8^{\frac{2}{3}} \] **Step 3:** Express 8 as a power of 2: \[ 8 = 2^3 \] Substitute into the equation: \[ m = \left(2^3\right)^{\frac{2}{3}} \] **Step 4:** Simplify the right-hand side using the power rule again: \[ m = 2^{3 \cdot \frac{2}{3}} = 2^2 = 4 \] Thus, the value of \( m \) is \( 4 \).