What is (10^3)^2?

What is (10^3)^2?

To calculate (10^3)^2, follow these steps:

1. Calculate 10^3, which equals 1,000.
2. Square the result from step 1 by multiplying it by itself: 1,000 x 1,000 = 1,000,000.

So, (10^3)^2 is equal to 1,000,000.

Evaluating Exponents with Exponents

In algebra, we can have expressions with exponents containing other exponents, like (10^3)^2. Evaluating these requires careful application of the order of operations and rules for exponents to simplify.

Let’s examine how to simplify (10^3)^2:

Review Exponent Rules

Some key rules for working with exponents:

• Product Rule: am • an = am+n
• Power Rule: (am)n = am•n
• When adding exponents, multiply the powers
• When multiplying exponents, add the powers

Applying Order of Operations

The innermost exponent gets evaluated first:

(10^3)^2

10^3 means 10 * 10 * 10 = 1,000

So the expression becomes:

(1,000)^2

Now we can evaluate the outer exponent:

(1,000)^2 = 1,000 * 1,000 = 1,000,000

Therefore, (10^3)^2 = 1,000,000 when fully simplified.

Checking the Work

We can verify this by entering the original expression into a calculator, which will also give 1,000,000 as the result. Getting the same solution confirms the order of operation and exponent rule application was correct.

Learning to parse expressions with exponents nested inside exponents builds proficiency with algebraic order of operations. Mastering the exponent rules allows simplifying complex exponential terms systematically.

In summary, use the order of operations to evaluate innermost exponents first. Then apply exponent rules to simplify outer exponents until the expression is reduced to a single term.