What you’ll learn
Apply power-of-a-power rule.
Key idea
A power of a power multiplies exponents; it is not a product of two separate same-base powers.
A nested power repeats an entire power and multiplies exponents; inverse outer exponent is nonzero.
Worked example
Enter the exact value or ordered values in the format requested below.
Rewrite (2^(-2))^5 as 2^n. Enter exponent n.
- The outer exponent 5 repeats the entire inner power 2^(-2) in a product.
- Multiply exponents -2×5=-10; the inverse equation 5x=-10 gives x=-2.
Answer: -10
Quick Check
Evaluate a worked attempt at apply power-of-a-power rule, identify the first invalid step, and provide the correction.
Step 1 identifies inner exponent -5 and outer exponent 3 in (3^(-5))^3. Step 2 adds them to claim 3^(-2). Locate the first invalid step and correct it.