Product and Powers Laws

Front

What is the Product Law of Exponents?

Back

The Product Law states that when multiplying two expressions with the same base, you add the exponents. For example, a^m * a^n = a^(m+n).

Front

What is the Power of a Power Law?

Back

The Power of a Power Law states that when raising a power to another power, you multiply the exponents. For example, (a^m)^n = a^(m*n).

Front

Simplify: (5x^3y^2)^2(2xy)

Back

50x^7y^5

Front

Simplify the exponential expression: 2^3 * 2^2

Back

2^5 = 32

Front

What is the Coefficient in a term?

Back

The coefficient is the numerical factor in a term. For example, in 4x^2, 4 is the coefficient.

Front

How do you simplify (2x^5)(6x^4)?

Back

Multiply coefficients (2*6=12) and add exponents (5+4=9), resulting in 12x^9.

Front

Simplify: (2x^3y)^6

Back

64x^18y^6

Front

What is the Power Law of Exponents?

Back

The Power Law states that when raising a base to an exponent, the exponent applies to both the base and any factors. For example, (ab)^n = a^n * b^n.

Front

Simplify: (-2mn)(3m^2n^4)^2

Back

-18m^5n^9

Front

What is the Zero Exponent Rule?

Back

Any non-zero base raised to the power of zero equals one. For example, a^0 = 1.