Final answer:
To simplify 23/5 × 27/10, we first find a common denominator for the fractions in the exponents and then add the exponents together since the bases are the same, resulting in the simplified form 213/10.
Step-by-step explanation:
The question involves using the laws of exponents to simplify the expression 23/5 × 27/10. To simplify, we add the exponents when multiplying two powers with the same base according to the rules of exponents.
First, we convert the exponents into fractions with a common denominator to add them easily:
- 3/5 is equivalent to 6/10.
Now the expression looks like 26/10 × 27/10. Adding the exponents, we get:
2(6/10 + 7/10) = 213/10
To find the common denominator, we simply multiplied the numerator and denominator of the first exponent by 2, since 5 × 2 = 10. This gives us exponents with the same denominator (10), which allows us to add them together directly.
Finally, 213/10 is the simplified form of the expression using the laws of exponents.