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 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 an expression with a base raised to a power multiplied by another base raised to a power?

Back

If the bases are the same, add the exponents: a^m * a^n = a^(m+n). If the bases are different, you cannot combine them.

Front

What is the simplified form of 4^2 * 4^3?

Back

4^2 * 4^3 = 4^(2+3) = 4^5 = 1024.

Front

What is the simplified form of 7p^0?

Back

7p^0 = 7 * 1 = 7.

Front

How do you simplify x^10 * x^4?

Back

x^10 * x^4 = x^(10+4) = x^14.

Front

What is the simplified form of (5p^9q^3)(2pq^7)?

Back

(5p^9q^3)(2pq^7) = 10p^(9+1)q^(3+7) = 10p^10q^10.