Laws of Exponents

Front

What is the law of exponents for a negative exponent?

Back

a^(-n) = 1/(a^n) for any non-zero number a.

Front

What happens when you raise a number to the power of zero?

Back

Any non-zero number raised to the power of zero equals 1.

Front

What is the product of powers rule?

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?

Back

When raising a power to another power, multiply the exponents: (a^m)^n = a^(m*n).

Front

What is the quotient of powers rule?

Back

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

Front

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

Back

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

Front

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

Back

6x^(2+3) = 6x^5.

Front

What is the law of exponents for multiplying powers with different bases?

Back

You cannot combine them; you can only simplify if they have the same base.

Front

Simplify: (3a^2b)(4ab^3)

Back

12a^(2+1)b^(1+3) = 12a^3b^4.

Front

What is the law of exponents for raising a product to a power?

Back

(ab)^n = a^n * b^n.