Simplify each expression. (4²)(4⁸)

Verified step by step guidance

1. Identify the base and the exponents in the expression \((4^{2})(4^{8})\). Both terms have the same base, which is 4.
2. Recall the exponent rule for multiplying powers with the same base: \(a^{m} \times a^{n} = a^{m+n}\).
3. Apply the rule by adding the exponents: \$4^{2} \times 4^{8} = 4^{2+8}$.
4. Simplify the exponent sum: \$4^{2+8} = 4^{10}$.
5. Express the simplified form as \$4^{10}$, which is the product of the original expression in exponential form.

Key Concepts

Laws of Exponents

The laws of exponents provide rules for simplifying expressions involving powers. One key rule states that when multiplying two expressions with the same base, you add their exponents: a^m * a^n = a^(m+n). This allows simplification of expressions like (4^2)(4^8) by adding the exponents 2 and 8.

Base Consistency in Exponentiation

For exponent rules to apply directly, the bases must be the same. In the expression (4^2)(4^8), both terms have the base 4, which allows the exponents to be combined. If the bases differ, the expression cannot be simplified by adding exponents.

Simplification of Exponential Expressions

Simplifying exponential expressions involves applying exponent rules to rewrite the expression in a simpler form. After combining exponents, the expression can be evaluated or left in exponential form, depending on the problem's requirements.