Power Rule of Exponents

Front

What is the Power Rule of 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: \( (5y^3z^2)^5 \)

Back

\( 5^5y^{15}z^{10} \)

Front

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

Back

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

Front

Which expression is equivalent to \( (2x)^3 \)?

Back

\( (2x)(2x)(2x) \)

Front

Simplify: \( ((9.2)^3)^7 \)

Back

\( 9.2^{21} \)

Front

Simplify: \( (m^3)^5 \)

Back

\( m^{15} \)

Front

What does it mean to simplify an expression using exponents?

Back

To simplify an expression using exponents means to reduce it to its simplest form by applying exponent rules.

Front

If \( a = 2 \) and \( b = 3 \), what is \( (ab)^2 \)?

Back

\( (2 \cdot 3)^2 = 6^2 = 36 \)

Front

What is the result of \( (x^2y^3)^4 \)?

Back

\( x^{8}y^{12} \)

Front

How do you simplify \( (a^m)(a^n) \)?

Back

You add the exponents: \( a^{m+n} \).