Exponent Rules Algebra

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

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 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.

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

Simplify: (x^3)(x^4)

Back

x^(3+4) = x^7.

Front

Simplify: (2x^2)(3x^5)

Back

6x^(2+5) = 6x^7.

Front

Simplify: (a^2b^3)(ab^2)

Back

a^(2+1)b^(3+2) = a^3b^5.

Front

Simplify: (5x^2)^3

Back

5^3 * x^(2*3) = 125x^6.