Question

Simplify the given expression:
3^(16 + (-12) + 28) * 2^(-10 + (-8)) * 1

Answer 1

To simplify 3^(16 + (-12) + 28) * 2^(-10 + (-8)) * 1, we add the exponents within each base, ignore the multiplication by 1 as it does not change the value, and express the simplified expression as 3^32 * 2^-18.

Step-by-step explanation:

To simplify the given expression, we need to follow the rules of exponentiation and multiplication. Let's break down the expression:

316 + (-12) + 28 * 2-10 + (-8) * 1

First, we simplify the exponents within the powers of 3 and 2:

For 316 + (-12) + 28, we add the exponents: 16 - 12 + 28 = 32. So we have 332.

For 2-10 + (-8), we add the exponents: -10 - 8 = -18. So we have 2-18.

Multiplying any number by 1 does not change the value, so the '* 1' part does not affect our simplification process.

Now we just multiply the two terms we've simplified:

332 * 2-18

Since there are no common bases or further simplifications that can be made easily, this is the most simplified form we can express without actual calculation. Thus, the simplified expression is 332 * 2-18.