Power of a Power Property

Front

What is the Power of a Power Property in exponents?

Back

The Power of a Power Property states that when raising a power to another power, you multiply the exponents: (a^m)^n = a^(m*n).

Front

Calculate (x^5)^2 using the Power of a Power Property.

Back

(x^5)^2 = x^(5*2) = x^{10}.

Front

What is the result of (2a^7b^2c)^3?

Back

(2a^7b^2c)^3 = 2^3 * (a^7)^3 * (b^2)^3 * (c)^3 = 8a^{21}b^6c^3.

Front

How do you simplify (x^{10})^3 * (x^2)^4?

Back

Using the Power of a Power Property: (x^{10})^3 * (x^2)^4 = x^{10*3} * x^{2*4} = x^{30} * x^{8} = x^{30+8} = x^{38}.

Front

What is the result of (-3x^7)^2?

Back

(-3x^7)^2 = (-3)^2 * (x^7)^2 = 9x^{14}.

Front

Calculate (-2x^6)^3 using the Power of a Power Property.

Back

(-2x^6)^3 = (-2)^3 * (x^6)^3 = -8x^{18}.

Front

What is the general formula for multiplying powers with the same base?

Back

When multiplying powers with the same base, you add the exponents: a^m * a^n = a^(m+n).

Front

Explain how to handle negative bases when applying the Power of a Power Property.

Back

When raising a negative base to an even exponent, the result is positive; when raised to an odd exponent, the result is negative.

Front

What is the result of (a^m)^n when a = 2, m = 3, and n = 4?

Back

(2^3)^4 = 2^(3*4) = 2^{12}.

Front

How do you simplify (x^3)^4 * (x^5)^2?

Back

Using the Power of a Power Property: (x^3)^4 * (x^5)^2 = x^{3*4} * x^{5*2} = x^{12} * x^{10} = x^{12+10} = x^{22}.