Properties of Exponents (and Radicals!)

Front

What is the value of any non-zero number raised to the power of 0?

Back

The value is 1.

Front

What is the result of raising a product to the power of 0, such as (ab)^0?

Back

The result is 1.

Front

How do you simplify an expression with a negative exponent, such as x^{-n}?

Back

You can rewrite it as 1/(x^n).

Front

What is the product of two powers with the same base, such as x^a * x^b?

Back

You add the exponents: x^(a+b).

Front

How do you simplify a power of a power, such as (x^a)^b?

Back

You multiply the exponents: x^(a*b).

Front

What is the quotient of two powers with the same base, such as x^a / x^b?

Back

You subtract the exponents: x^(a-b).

Front

How do you simplify the expression (x^m)(y^n)?

Back

You multiply the coefficients and keep the variables separate: (x^m)(y^n) = xy^(n) * x^(m).

Front

What is the result of simplifying (a^m)(a^n)?

Back

The result is a^(m+n).

Front

How do you simplify the expression (x^2y^3)^4?

Back

You distribute the exponent: x^(2*4)y^(3*4) = x^8y^12.

Front

What is the simplified form of (2m^4)(5m^2)?

Back

The simplified form is 10m^6.