write 100 and 72 as products of two powers
100 = 10^2 = (2*5)^2 = 2^2 * 5^2
72 = 8*9 = 2^3 * 3^2
2^2
To write 100 as a product of two powers, we can start by finding the prime factors of 100, which are 2 and 5.
Next, we rewrite 100 as a product of these prime factors:
100 = 2^2 × 5^2
Therefore, 100 can be written as a product of two powers as 2 raised to the power of 2, multiplied by 5 raised to the power of 2.
Now, let's write 72 as a product of two powers. Similarly, we find the prime factors of 72, which are 2, 2, 2, 3, and 3.
We can express 72 as a product of these prime factors:
72 = 2^3 × 3^2
Hence, 72 can be written as a product of two powers as 2 raised to the power of 3, multiplied by 3 raised to the power of 2.
Therefore, 100 can be written as 2^2 × 5^2, and 72 can be written as 2^3 × 3^2.