What you’ll learn
Work with powers of ten.
Key idea
A power uses repeated factors or their reciprocal; a zero exponent on nonzero base gives the multiplicative identity.
Negative powers are reciprocals, zero power is identity; exponentiation is not base-times-exponent.
Worked example
Enter the exact value or ordered values in the format requested below.
Evaluate 10^(4) as an exact decimal. Enter the value without rounding.
- 10^(4)=10000: moving through integer powers changes place value by a factor of ten per exponent step.
- Exponent 4 counts positive factors of ten; it is not ordinary multiplication 10×(4).
Answer: 10000
Quick Check
Evaluate a worked attempt at work with powers of ten, identify the first invalid step, and provide the correction.
Step 1 reads integer exponent 5 in 10^(5). Step 2 treats it as multiplier and reports 10×(5)=50. Identify the first invalid step and correct the value.