Question

Simplify the following expression using both propertiesof exponents and using expansion of the expression. Show all work .

Answer 1

To simplify exponential expressions, multiply the numeric coefficients separately and add exponents for like bases. For example, 3.2 × 10³ times 2 × 10² simplifies to 6.4 × 10µ, and (5³)⁴ simplifies to 5¹².

Step-by-step explanation:

Simplifying Exponential Expressions

To simplify an exponential expression like 3.2 × 10³ times 2 × 10², we use the rules of multiplication of exponentials. According to these rules, we multiply the digit terms (3.2 and 2) together, and then add the exponents when the bases are the same (10³ and 10²). Here is how the simplification works step-by-step:

1. Multiply the numeric coefficients: 3.2 × 2 = 6.4.
2. Add the exponents of like bases: 10³ × 10² = 10³+2 = 10µ.
3. Combine these results to get the simplified expression: 6.4 × 10µ.

When we simplify expressions that involve raising an exponent to another exponent, like (5³)⁴, each factor inside the parentheses is raised to the outer exponent. This results in the exponents being multiplied:

1. Recognize that (5³)⁴ is (5 × 5 × 5)⁴.
2. Multiply the exponents: 3 × 4 = 12.
3. So the simplified expression is 5¹².