Final answer:
The expression equivalent to 32x8,10 can be found by re-expressing 32 using properties of exponents. One way is to reframe 32 as 24×10¹², then multiply the prefactor by 10 and decrease the exponent, resulting in 3×10µ when simplified, using the base knowledge of powers of ten.
Step-by-step explanation:
To find an expression equivalent to 32x8,10, we can use the properties of exponents and multiplication. First, we recognize that 24 is divisible by 8, and we can reframe 32 as 24×10¹². By doing this, we multiply the prefactor by 10 and reduce the exponent by one, which does not change the value of the expression: 2×10¹²−7, simplifying to 3×10µ.
Another approach is to fall back on the basics of powers of 10. For instance, 10¹° simplifies to 1, as 10¹° is equal to 1. Similarly, 10⁻⁴, through repeated application of 10⁻¹, would lead to 0.0001. Hence, understanding integer powers can greatly assist in simplifying expressions involving powers of ten.
When multiplying powers of ten, one should remember that the powers should be added. Thus, for example, 10² × 10³ would equal 10⁵. Using this principle, we can manipulate the expressions and solve the problem without converting into scientific notation.