Exponents & Radicals redo

Front

What is the simplest radical form of the expression -4√75 - √24 + 7√12?

Back

-6√3 - 2√6

Front

Simplify the expression (-\frac{1}{2}c^{-3}d^{-8})^2 \cdot (-6c^2d)^3 and write in simplest terms with all positive exponents.

Back

-\frac{54}{d^{13}}

Front

Simplify the expression \frac{k^{-\frac{1}{4}} \cdot k^{\frac{9}{2}}}{k^{-2}} and write in simplest radical form with a rational denominator.

Back

k^{ } \sqrt[4]{k}

Front

What is the equivalent expression for \left(\frac{a}{b}\right)^n?

Back

\frac{a^n}{b^n}

Front

What is the equivalent expression for b^m ⋅ b^n?

Back

b^{m + n}

Front

Define the term 'exponent'.

Back

An exponent is a number that indicates how many times to multiply the base by itself.

Front

What is the product of powers rule?

Back

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

Front

What is the power of a power rule?

Back

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

Front

What is the quotient of powers rule?

Back

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

Front

Define the term 'radical'.

Back

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