7.1 - 7.4 Exponent Rules (Basics)

Front

What is the product of two powers with the same base?

Back

When multiplying two powers with the same base, you add the exponents. For example, x^a ⋅ x^b = x^(a+b).

Front

What is the power of a power rule in exponents?

Back

When raising a power to another power, you multiply the exponents. For example, (x^a)^b = x^(a*b).

Front

How do you simplify a quotient of powers with the same base?

Back

When dividing two powers with the same base, you subtract the exponents. For example, x^a / x^b = x^(a-b).

Front

What is the value of (-5p)^2?

Back

The value of (-5p)^2 is 25p^2.

Front

How do you simplify x^8 / x^2?

Back

To simplify x^8 / x^2, subtract the exponents: x^(8-2) = x^6.

Front

What is the result of (m^9)^2?

Back

The result of (m^9)^2 is m^(9*2) = m^18.

Front

How do you simplify k^3 / 5k?

Back

To simplify k^3 / 5k, divide the coefficients and subtract the exponents: k^(3-1) / 5 = k^2 / 5.

Front

What is the zero exponent rule?

Back

Any non-zero base raised to the power of zero equals one: x^0 = 1 (for x ≠ 0).

Front

What is the negative exponent rule?

Back

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent: x^(-a) = 1/x^a.

Front

What is the definition of an exponent?

Back

An exponent indicates how many times a number (the base) is multiplied by itself. For example, x^n means x is multiplied by itself n times.