Exponents Power Rule

Front

What is the Power Rule for exponents?

Back

The Power Rule states that when raising a power to another power, you multiply the exponents. For example, \( (a^m)^n = a^{m \cdot n} \).

Front

Simplify: \( (5^2c^3)^5 \)

Back

\( 5^{10}c^{15} \)

Front

What is the result of \( (4yx^4)^2 \)?

Back

\( 16y^2x^8 \)

Front

Simplify: \( (3x^3y^5)^4 \)

Back

\( 81x^{12}y^{20} \)

Front

What is the simplified form of \( (3x^4y^5)^2 \)?

Back

\( 9x^8y^{10} \)

Front

Find the missing exponent value in \( (2^?)^5=2^{15} \)

Back

3

Front

If \( a^m \cdot a^n = ? \), what is the result?

Back

\( a^{m+n} \) (Add the exponents)

Front

What does \( a^0 \) equal for any non-zero number \( a \)?

Back

1 (Any non-zero number raised to the power of zero is 1)

Front

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

Back

\( x^3y^6 \) (Apply the Power Rule to each factor)

Front

If \( (ab)^n = ? \), what is the result?

Back

\( a^n b^n \) (Distribute the exponent to each factor)