Solve for a (6x^2)(4x^2)=a*x^b

$(6 x^{2}) (4 x^{2}) = a \cdot x^{b}$

Rewrite the equation as $a \cdot x^{b} = 6 x^{2} (4 x^{2})$ .

$a \cdot x^{b} = 6 x^{2} (4 x^{2})$

Simplify.

Multiply $4$ by $6$ .

$a \cdot x^{b} = 24 x^{2} x^{2}$

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$a \cdot x^{b} = 24 (x^{2} x^{2})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$a \cdot x^{b} = 24 x^{2 + 2}$

Add $2$ and $2$ .

$a \cdot x^{b} = 24 x^{4}$

Divide each term in $(a \cdot x^{b}) = 24 x^{4}$ by $x^{b}$ and simplify.

Divide each term in $(a \cdot x^{b}) = 24 x^{4}$ by $x^{b}$ .

$\frac{(a \cdot x^{b})}{x^{b}} = \frac{24 x^{4}}{x^{b}}$

Simplify the left side.

Cancel the common factor of $x^{b}$ .

Cancel the common factor.

$\frac{a \cdot x^{b}}{x^{b}} = \frac{24 x^{4}}{x^{b}}$

Divide $a$ by $1$ .

$a = \frac{24 x^{4}}{x^{b}}$

Simplify the right side.

Cancel the common factor of $x^{4}$ and $x^{b}$ .

Factor $x^{b}$ out of $24 x^{4}$ .

$a = \frac{x^{b} (24 x^{4 - b})}{x^{b}}$

Cancel the common factors.

Multiply by $1$ .

$a = \frac{x^{b} (24 x^{4 - b})}{x^{b} \cdot 1}$

Cancel the common factor.

$a = \frac{x^{b} (24 x^{4 - b})}{x^{b} \cdot 1}$

Rewrite the expression.

$a = \frac{24 x^{4 - b}}{1}$

Divide $24 x^{4 - b}$ by $1$ .

$a = 24 x^{4 - b}$