U5 CFA 2 Radicals

Front

What is the fractional exponent representation of \(\sqrt{7}\)?

Back

\(7^{\frac{1}{2}}\)

Front

What does \(x^{-1}\) equal?

Back

\(\frac{1}{x}\) (Negative exponents are 'flipped' to the bottom)

Front

Simplify \(\frac{x^{1-a}}{x^a}\).

Back

\(x^{1-2a}\)

Front

Simplify \(\frac{t^{12}}{t^2}\).

Back

\(t^{10}\) (Use subtraction when dividing exponents with the same base)

Front

Rewrite \(\sqrt[3]{x^5}\).

Back

\(x^{\frac{5}{3}}\)

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 rule for multiplying exponents with the same base?

Back

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

Front

What is the rule for dividing exponents with the same base?

Back

Subtract the exponents: \(\frac{a^m}{a^n} = a^{m-n}\)

Front

What is the definition of a negative exponent?

Back

A negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent: \(a^{-n} = \frac{1}{a^n}\)

Front

What is the fractional exponent representation of \(\sqrt[4]{x}\)?

Back

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