Power of Powers

Front

What is the Power of a Power Rule in exponents?

Back

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

Front

Simplify: (3^2)^4

Back

3^(2*4) = 3^8.

Front

What is the result of (x^5)^3?

Back

x^(5*3) = x^15.

Front

Simplify: (a^3)^2

Back

a^(3*2) = a^6.

Front

What does it mean to raise a negative exponent?

Back

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

Front

Simplify: (2^-3)^2

Back

(2^-3)^2 = 2^(-3*2) = 2^-6 = 1/(2^6).

Front

What is the result of (5^2)(5^3)?

Back

Add the exponents: 5^(2+3) = 5^5.

Front

What is the result of (x^2)(x^4)?

Back

Add the exponents: x^(2+4) = x^6.

Front

Simplify: (y^4)(y^-2)

Back

y^(4-2) = y^2.

Front

What is the result of (2^3)^2?

Back

2^(3*2) = 2^6.