Algebra II - Chapter 8 Review

Front

What is the opposite of a cube root (\( ^3\sqrt{ } \))?

Back

Cubing

Front

Simplify \( \left(a^{\frac{1}{2}}\right)^{\frac{2}{3}} \)

Back

\( a^{\frac{1}{3}} \)

Front

Simplify \( \left(8x^9\right)^{-\frac{2}{3}} \)

Back

\( \frac{1}{4x^6} \)

Front

Simplify \( \sqrt[]{45x^4y^7} \)

Back

\( 3x^2y^3\sqrt[]{5y} \)

Front

Re-write the expression in radical form: \( \left(3n\right)^{\frac{1}{2}} \)

Back

\( \sqrt[]{3n} \)

Front

What is the definition of a radical?

Back

A radical is an expression that includes a root, such as a square root or cube root.

Front

What is the product rule for exponents?

Back

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

Front

What is the power of a power rule for exponents?

Back

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

Front

What is the quotient rule for exponents?

Back

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

Front

What is the definition of a rational exponent?

Back

A rational exponent is an exponent that is a fraction, indicating both a power and a root: \( a^{\frac{m}{n}} = \sqrt[n]{a^m} \)