A mathematics teacher bought a birthday cake for his son with the dedication
Happy (2 raise to 5/2 .(the dot means times) 2 raise to 3/4 divided by 2 raise to 1/4)
Birthday!!!
How old is his son?
kindly help me...
2^(5/2) * 2^(3/4) / 2^(1/4) = 2^(5/2 + 3/4 - 1/4) = 2^3 = 8
Well, let's break it down!
The dedication on the cake is Happy (2^(5/2) * 2^(3/4) / 2^(1/4)) Birthday!!!.
To simplify this, we can use the laws of exponents. When you multiply numbers with the same base, you add their exponents.
So, let's add the exponents:
(5/2) + (3/4) - (1/4)
Hmm, that's a tricky one. Let's convert all the fractions to a common denominator, which is 4.
So, now we have:
(10/4) + (3/4) - (1/4)
Adding these fractions together, we get:
(10 + 3 - 1)/4
= 12/4
= 3
So, the dedication on the cake simplifies to 2^3, which is equal to 8.
Therefore, the math teacher's son is 8 years old.
Hope that helps, and happy math-ing!
To find out the age of the son, we need to simplify the expression inside the dedication.
Let's simplify the expression step-by-step:
Step 1: Simplify the exponents:
2^(5/2) * 2^(3/4) / 2^(1/4)
Step 2: Apply the exponent rule for multiplication:
2^(5/2 + 3/4) / 2^(1/4)
Step 3: Convert the mixed numbers to improper fractions:
2^(10/4 + 3/4) / 2^(1/4)
Step 4: Simplify the exponents:
2^(13/4) / 2^(1/4)
Step 5: Apply the exponent rule for division:
2^(13/4 - 1/4)
Step 6: Simplify the exponents:
2^(12/4)
Step 7: Simplify the fraction:
2^3
Step 8: Evaluate the expression:
8
Therefore, the birthday dedication simplifies to "Happy 8th Birthday!!!". So, the son is 8 years old.
To determine the age of the son, we need to solve the given mathematical expression. Let's break it down step by step:
Happy (2^(5/2) * 2^(3/4) / 2^(1/4)) Birthday!!!
We can simplify this expression using the properties of exponents. Recall that when dividing with the same base, you subtract the exponents:
2^(5/2) * 2^(3/4) / 2^(1/4)
= 2^((5/2) + (3/4) - (1/4))
Now, let's add the fractions inside the parentheses:
= 2^((5/2) + (2/4))
Next, let's find a common denominator for the two fractions:
= 2^((5/2) + (1/2))
Since the fractions now have a common denominator of 2, we can add the numerators:
= 2^((5 + 1) / 2)
= 2^(6/2)
= 2^(3/1)
= 2^3
= 8
Therefore, the age of the son is 8 years.