Laws of exponents pt 2

Front

What is the power of a power rule in exponents?

Back

When raising a power to another power, multiply the exponents: \( (a^m)^n = a^{m \cdot n} \).

Front

Simplify the expression \( (x^3)^7 \).

Back

\( x^{21} \) (using the power of a power rule).

Front

What is the square root of a number?

Back

The square root of a number \( x \) is a value \( y \) such that \( y^2 = x \).

Front

Simplify \( \sqrt{9} \).

Back

3.

Front

What is the product of powers rule in exponents?

Back

When multiplying two powers with the same base, add the exponents: \( a^m \cdot a^n = a^{m+n} \).

Front

Simplify \( 4\sqrt{75} \).

Back

\( 20\sqrt{3} \).

Front

What is the quotient of powers rule in exponents?

Back

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

Front

Simplify \( \frac{(6x^2y)^2}{3} \).

Back

\( 24x^4y^2 \) (using the power of a product rule and simplifying).

Front

What is the power of a product rule in exponents?

Back

When raising a product to a power, raise each factor to the power: \( (ab)^n = a^n b^n \).

Front

Simplify \( \sqrt{147} \).

Back

\( 7\sqrt{3} \).