Exponent Rules

Front

What is the product of powers rule in exponentiation?

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^10 ⋅ x^4?

Back

By applying the product of powers rule, you add the exponents: x^(10+4) = x^14.

Front

What is the power of a power rule in exponentiation?

Back

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

Front

How do you simplify (4^2)(4^3)?

Back

By applying the product of powers rule, you add the exponents: 4^(2+3) = 4^5 = 1024.

Front

What is the power of a product rule in exponentiation?

Back

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

Front

How do you simplify (-5p)^2?

Back

By applying the power of a product rule: (-5)^2 * p^2 = 25p^2.

Front

What is the quotient of powers rule in exponentiation?

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 x^8 / x^2?

Back

By applying the quotient of powers rule: x^(8-2) = x^6.

Front

What is the product of powers rule for negative bases?

Back

The product of powers rule applies the same way: (-a)^m * (-a)^n = (-a)^(m+n).

Front

How do you simplify (5p^9q^3)(2pq^7)?

Back

By applying the product of powers rule: 5*2 * p^(9+1) * q^(3+7) = 10p^10q^10.