What you’ll learn
Apply product rule for integer exponents.
Key idea
Multiplying powers of the same nonzero base adds their signed exponents, rather than multiplying exponents.
Same-base products add signed exponents; numbers changing do not create an additional form.
Worked example
Enter the exact value or ordered values in the format requested below.
Rewrite 2^(-4)×2^(1) as 2^n. Enter exponent n.
- For nonzero common base 2, powers multiply by adding signed exponents: -4+(1)=-3.
- Thus 2^(-4)×2^(1)=2^(-3); the missing first exponent solves x+(1)=-3, so x=-4.
Answer: -3
Quick Check
Evaluate a worked attempt at apply product rule for integer exponents, identify the first invalid step, and provide the correction.
Step 1: the bases of 2^(-1)×2^(-5) match and are nonzero. Step 2: multiply exponents to write 2^(5). Identify the first invalid step and correct the exponent.