Solve 12x^2:(-4x^2)=

$$12 x ^ { 2 } : ( - 4 x ^ { 2 } ) =$$

Evaluate

$$-3$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(12x^{2}\right)^{1}\times \frac{1}{-4x^{2}}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$12^{1}\left(x^{2}\right)^{1}\times \frac{1}{-4}\times \frac{1}{x^{2}}$$

Use the Commutative Property of Multiplication.

$$12^{1}\times \frac{1}{-4}\left(x^{2}\right)^{1}\times \frac{1}{x^{2}}$$

To raise a power to another power, multiply the exponents.

$$12^{1}\times \frac{1}{-4}x^{2}x^{2\left(-1\right)}$$

Multiply 2 times -1.

$$12^{1}\times \frac{1}{-4}x^{2}x^{-2}$$

To multiply powers of the same base, add their exponents.

$$12^{1}\times \frac{1}{-4}x^{2-2}$$

Add the exponents 2 and -2.

$$12^{1}\times \frac{1}{-4}x^{0}$$

Raise 12 to the power 1.

$$12\times \frac{1}{-4}x^{0}$$

Raise -4 to the power -1.

$$12\left(-\frac{1}{4}\right)x^{0}$$

Multiply 12 times -\frac{1}{4}.

$$-3x^{0}$$

For any term t except 0, t^{0}=1.

$$-3$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{12^{1}x^{2}}{\left(-4\right)^{1}x^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{12^{1}x^{2-2}}{\left(-4\right)^{1}}$$

Subtract 2 from 2.

$$\frac{12^{1}x^{0}}{\left(-4\right)^{1}}$$

For any number a except 0, a^{0}=1.

$$\frac{12^{1}}{\left(-4\right)^{1}}$$

Divide 12 by -4.

$$-3$$

Factor

$$-3$$