Exponents and Radicals review

Front

What is the product of powers rule in exponents?

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 in exponents?

Back

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

Front

What is the zero exponent rule?

Back

Any non-zero number raised to the power of zero equals one: a^0 = 1 (where a ≠ 0).

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, represented by the symbol √.

Front

What is the product of square roots rule?

Back

The product of two square roots can be expressed as the square root of the product: √a * √b = √(a*b).

Front

Simplify: (x^5)^4

Back

x^20.

Front

What is the quotient of powers rule in exponents?

Back

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

Front

What is the definition of a rational exponent?

Back

A rational exponent indicates both the power and the root: a^(1/n) = √a (the n-th root of a).

Front

Simplify: (x^5y^4z^3)^2

Back

x^10y^8z^6.

Front

What is the definition of an exponent?

Back

An exponent indicates how many times a number (the base) is multiplied by itself: a^n = a * a * ... * a (n times).