Exponent Rules

Front

What is the product of powers rule in exponents?

Back

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

Front

Simplify: 6x^2 ⋅ 2y^4 ⋅ x

Back

12x^3y^4

Front

What is the quotient of powers rule in exponents?

Back

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

Front

Simplify: (2^x^4y^5)(-3x^2y^7)

Back

-6x^6y^12

Front

What is the power of a power rule in exponents?

Back

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

Front

Simplify: (6x^2)(-3x^5)

Back

-18x^7

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

Simplify: r^6 ⋅ r^2 ⋅ r^3

Back

r^11

Front

What is the negative exponent rule?

Back

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

Front

Evaluate using the quotient rule: 7^6 / 7^1

Back

7^5