◂⋅▸5^8⋅5^4 /◂◽˙▸(5^3)^2
◂/▸ 2^9⋅◂◽˙▸(2^−2)^−3 / 2
which one is bigger and what is the difference between them
To solve these expressions, we need to simplify each one step by step:
◂⋅▸5^8⋅5^4 /◂◽˙▸(5^3)^2
First, simplify the exponents within each set of parentheses:
5^8 * 5^4 / (5^3)^2
Next, simplify the exponent within each set of parentheses:
5^8 * 5^4 / 5^6
Now, apply the exponent properties to combine the exponents:
5^(8 + 4 - 6)
Simplify the exponent:
5^6
The first expression simplifies to 5^6.
Next, let's solve the second expression:
◂/▸ 2^9⋅◂◽˙▸(2^−2)^−3 / 2
First, simplify the exponents within each set of parentheses:
2^9 * (2^-2)^-3 / 2
Next, simplify each set of parentheses:
2^9 * 2^6 / 2
Now, apply the exponent properties to combine the exponents:
2^(9 + 6 - 1)
Simplify the exponent:
2^14
The second expression simplifies to 2^14.
To compare which one is bigger, we can calculate the values of both expressions:
5^6 ≈ 15,625
2^14 ≈ 16,384
The second expression (2^14) is bigger than the first expression (5^6) by approximately 759, with the value of 16,384 - 15,625.