Laws of Exponents - Power to Power/Negative

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

Simplify: (2x^3y)^6

Back

64x^18y^6.

Front

What does a negative exponent represent?

Back

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent: a^(-n) = 1/(a^n).

Front

Simplify: (x^5)^4

Back

x^20.

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

Simplify: (3xy^2)^2(x^2y)^4

Back

9x^{10}y^8.

Front

What is the quotient of powers rule in exponents?

Back

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

Front

Simplify: x^{-4}

Back

1/x^4.

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

Simplify: (r^4)^6

Back

r^24.