Problem 15 - Algebra 1

Question

Evaluate the expression when \(x=3\) $$ 10^{x} $$

Step-by-Step Solution

Answer

Therefore, the value of the expression \(10^x\) when \(x=3\) is 1000.

Step 1: Substitute the Given Value

Replace \(x\) in the equation \(10^x\) with the given value, which in this case is 3. So, the equation becomes \(10^3\).

Step 2: Evaluate the Exponential Expression

\(10^3\) means '10 multiplied by itself 3 times'. In other words, it's \(10 * 10 * 10\), which equals to 1000.

Key Concepts

Exponents

Exponents are a unique way to express repeated multiplication of the same number. When we see an exponent, like in the expression \(10^3\), it tells us how many times to multiply the base number (10, in this case) by itself. The small number above and to the right (the exponent) is the number of times you perform this multiplication.Key things to remember about exponents:

• The base is the number that is being multiplied.
• The exponent indicates how many times the base is multiplied by itself.
• In \(10^3\), the base is 10, and the exponent is 3, meaning \(10 \times 10 \times 10\).

Exponents are powerful tools for simplifying expressions and are often used in scientific notation, technology, and various fields of mathematics and science.

Substitution

Substitution is a technique used in algebra where we replace variables with their given values or known quantities.In the exercise, substitution involves replacing \(x\) with the number 3 in the expression \(10^x\). By substituting, we transform the general expression into a specific numerical one, \(10^3\), which can then be easily evaluated.To effectively use substitution:

• Identify the variable in the expression.
• Replace the variable with the value provided.
• Ensure every instance of the variable is replaced to maintain consistency.

Substitution simplifies expressions, making them solvable and easier to understand.

Mathematical Operations

Mathematical operations are fundamental in solving expressions. They include addition, subtraction, multiplication, division, and exponentiation.In evaluating expressions like \(10^3\), our primary mathematical operation is exponentiation, which involves repeated multiplication.Steps to evaluate an expression using mathematical operations:

• Identify the operations present in the expression, such as exponents or basic arithmetic.
• Follow the order of operations (PEMDAS/BODMAS) to ensure accurate results. This means dealing with Parentheses/Brackets first, then Exponents/Orders, followed by Multiplication and Division, and finally Addition and Subtraction.
• Carry out the operations step by step until the expression is completely simplified.

Understanding mathematical operations allows for precise and correct computation of expressions like \(10^3\).