Rules of Exponents

Front

What is the product of powers rule in exponents?

Back

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

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

What is the power of a product rule in exponents?

Back

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

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 of the base raised to the opposite positive exponent: a^(-n) = 1/(a^n) (where a ≠ 0).

Front

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

Back

Using the product of powers rule, (x^5)(x^5) = x^(5+5) = x^10.

Front

What does it mean if (2^x)^5 = 2^15?

Back

This means that the exponents must be equal, so x*5 = 15, leading to x = 3.

Front

What is the result of multiplying (6x^2) and (-3x^5)?

Back

Multiply the coefficients and add the exponents: (6)(-3) = -18 and x^(2+5) = x^7, so the result is -18x^7.

Front

What is the quotient of powers rule in exponents?

Back

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

Front

What is the power of a quotient rule in exponents?

Back

When raising a quotient to a power, apply the exponent to both the numerator and the denominator: (a/b)^n = a^n / b^n.