Laws of Exponents

Front

What is the product of powers property in exponents?

Back

When multiplying two expressions with the same base, you add the exponents: a^m ∙ a^n = a^(m+n).

Front

How do you simplify x ∙ x ∙ x ∙ x ∙ x ∙ x?

Back

This simplifies to x^6, using the product of powers property.

Front

What is the quotient of powers property in exponents?

Back

When dividing two expressions with the same base, you subtract the exponents: a^m / a^n = a^(m-n).

Front

How do you simplify \frac{x^8y^7z^6}{x^5y^4z^3}?

Back

This simplifies to x^(8-5) y^(7-4) z^(6-3) = x^3y^3z^3 using the quotient of powers property.

Front

What is the power of a power property in exponents?

Back

When raising a power to another power, you multiply the exponents: (a^m)^n = a^(m*n).

Front

How do you simplify (3x^4)^5?

Back

This simplifies to 3^5 ∙ (x^4)^5 = 243x^20 using the power of a power property.

Front

What is the power of a product property in exponents?

Back

When raising a product to a power, you distribute the exponent: (ab)^n = a^n ∙ b^n.

Front

How do you simplify (-4r^5)(2r^8)?

Back

This simplifies to -4 ∙ 2 ∙ r^(5+8) = -8r^13 using the product of powers property.

Front

What is the zero exponent rule?

Back

Any non-zero base raised to the power of zero equals one: a^0 = 1 (where a ≠ 0).

Front

What is the negative exponent rule?

Back

A negative exponent indicates the reciprocal: a^(-n) = 1/a^n.