Multiplying and Dividing Exponents

Front

What is an exponent?

Back

An exponent is a mathematical notation indicating the number of times a number (the base) is multiplied by itself.

Front

What does it mean to multiply exponents with the same base?

Back

When multiplying exponents with the same base, you add the exponents. For example, a^m * a^n = a^(m+n).

Front

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

Back

When dividing exponents with the same base, you subtract the exponents. For example, a^m / a^n = a^(m-n).

Front

How do you simplify (-2)³ (-2)⁶?

Back

You add the exponents: (-2)^(3+6) = (-2)⁹.

Front

What is the result of (x²)³?

Back

You multiply the exponents: x^(2*3) = x⁶.

Front

What is the zero exponent rule?

Back

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

Front

What is the negative exponent rule?

Back

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

Front

How do you simplify (3x²)²?

Back

You apply the exponent to both the coefficient and the variable: (3²)(x^(2*2)) = 9x⁴.

Front

What is the power of a product rule?

Back

When raising a product to a power, you apply the exponent to each factor: (ab)ⁿ = aⁿbⁿ.

Front

What is the power of a quotient rule?

Back

When raising a quotient to a power, you apply the exponent to both the numerator and the denominator: (a/b)ⁿ = aⁿ/bⁿ.