Multiplication and division with exponents

Key Notes :

Multiplication with Exponents

  • Product Rule: When multiplying powers with the same base, add the exponents.
    • a^m * a^n = a^(m+n)
    • Example: 2³ * 2⁴ = 2^(3+4) = 2⁷
  • Multiplying Powers with Different Bases: If the bases are different, you cannot combine the exponents directly.
    • Example: 3² * 5⁴ cannot be simplified further.

Division with Exponents

  • Quotient Rule: When dividing powers with the same base, subtract the exponents.
    • a^m / a^n = a^(m-n)
    • Example: 4⁵ / 4² = 4^(5-2) = 4³
  • Dividing Powers with Different Bases: If the bases are different, you cannot combine the exponents directly.
    • Example: 6³ / 2² cannot be simplified further.

Learn with an example

Simplify. Express your answer using positive exponents.

n7 . n–9/n8 = _______

First, simplify the numerator.

n7 . n-9 / n8

n7 + -9 / n8 Multiply, remembering to add the exponents

n-2 / n8

The numerator is simplified. Now, divide the numerator by the denominator.

n-2 – 8 Divide, remembering to subtract the exponents

n-10

Finally , express your answer using positive exponents

n-10

1 / n10

Simplify. Express your answer using positive exponents.

u–6 . u–8 . u3 = _________

Simplify.

u-6 . u-8 u3

u-6 + -8 +3 Multiply, remembering to add the exponents

u-11

Finally , express your answer using positive exponents

u-11

1 / u11

Simplify. Express your answer using positive exponents.

b6 . b–4 / b-9 = ______

First, simplify the numerator.

b6 . b–4/b–9

b6+–4/b–9 Multiply, remembering to add the exponents

b2/b–9 The numerator is simplified. Now, divide the numerator by the denominator.

b2– –9 Divide, remembering to subtract the exponents

b11

let’s practice!