Rules of exponents

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 the expression: x^5 * x^7

Back

x^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 the expression: (-4r^5) * (2r^8)

Back

-8r^13

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 the expression: 15^9 / 15^3

Back

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

Simplify the expression: (-2)^3 * (-2)^6

Back

(-2)^9

Front

What is the negative exponent rule?

Back

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

Front

Simplify the expression: x^2 / x^5

Back

x^(-3) or 1/x^3.