1.5 Advanced Laws of Exponents

Step 1

Use the law $a^x b^x = (ab)^x$ .

Step 2

$2^x \cdot 5^x = (2 \cdot 5)^x = 10^x$ .

Step 3

Rewrite 1000 as a power of 10: $1000 = 10^3$ .

Step 4

$10^x = 10^3 \implies x = 3$ .

Final Answer

Operation

Number

Quick Reference:

N = Natural Numbers: 1, 2, 3, ...

W = Whole Numbers: 0, 1, 2, ...

Z = Integers: ..., -2, -1, 0, 1, 2, ...

Q = Rational Numbers: p/q form (p, q ∈ Z, q ≠ 0)

R = Real Numbers: Q ∪ Irrational

Select an operation and enter values to see detailed step-by-step solutions.