Rules of Exponents

Front

What is the product of two powers with the same base?

Back

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

Front

How do you simplify the expression (x^5)(x^5)?

Back

You add the exponents: (x^5)(x^5) = x^(5+5) = x^10.

Front

What is the power of a power rule 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 the expression (5^3)^7?

Back

You multiply the exponents: (5^3)^7 = 5^(3*7) = 5^21.

Front

What is the quotient of two powers with the same base?

Back

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

Front

How do you simplify the expression 15^9 ÷ 15^3?

Back

You subtract the exponents: 15^9 ÷ 15^3 = 15^(9-3) = 15^6.

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 happens when you raise a product to a power?

Back

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

Front

How do you simplify the expression (7y^4)^2?

Back

You apply the power of a power rule: (7y^4)^2 = 7^2 * (y^4)^2 = 49y^(4*2) = 49y^8.

Front

What is the negative exponent rule?

Back

A negative exponent indicates the reciprocal: a^(-n) = 1/(a^n) (where a ≠ 0).