Exponent Rules

Front

What is the product of powers rule in exponentiation?

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 exponentiation?

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 exponentiation?

Back

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

Front

What is the power of a quotient rule in exponentiation?

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.

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.

Front

How do you simplify (2a^3b^4c^3)^2?

Back

Apply the power of a product rule: (2^2)(a^(3*2))(b^(4*2))(c^(3*2)) = 4a^6b^8c^6.

Front

How do you simplify (m^9)^2?

Back

Use the power of a power rule: m^(9*2) = m^18.

Front

How do you simplify 10x^8 * 9x?

Back

Multiply the coefficients and add the exponents: (10*9)(x^(8+1)) = 90x^9.

Front

How do you rewrite w^(-13) using a positive exponent?

Back

Use the negative exponent rule: w^(-13) = 1/w^13.