\( 4\left(a^{2}\right)^{2} \times\left(a^{3}\right)^{2} \) \( =\frac{\left(a^{2}\right)^{2}}{\left(a^{3}\right)^{0}} \) (c) \( 10\left(x^{2}\right)^{2} \)

1. For the expression \[ 4\left(a^{2}\right)^{2} \times\left(a^{3}\right)^{2} \] we first apply the power-of-a-power rule: \[ \left(a^2\right)^2 = a^{2 \times 2} = a^4, \quad \left(a^3\right)^2 = a^{3 \times 2} = a^6. \] Then, the expression becomes: \[ 4a^4 \times a^6. \] Using the product of powers rule, we add the exponents: \[ a^4 \times a^6 = a^{4+6} = a^{10}. \] So the simplified result is: \[ 4a^{10}. \] 2. For the expression \[ \frac{\left(a^{2}\right)^{2}}{\left(a^{3}\right)^{0}}, \] first simplify the numerator: \[ \left(a^2\right)^2 = a^{2 \times 2} = a^4. \] Next, note that any nonzero number raised to the 0th power is 1: \[ \left(a^3\right)^0 = 1. \] Thus, the expression becomes: \[ \frac{a^4}{1} = a^4. \] 3. For the expression \[ 10\left(x^{2}\right)^{2}, \] apply the power-of-a-power rule: \[ \left(x^2\right)^2 = x^{2 \times 2} = x^4. \] Multiply by 10: \[ 10x^4. \] The final answers are: - \(4(a^2)^2 \times (a^3)^2 = 4a^{10}\), - \(\frac{(a^2)^2}{(a^3)^0} = a^4\), - \(10(x^2)^2 = 10x^4\).