Determine whether each statement is true or false. If false, correct the right side of the equation. (y^2)(y^5) = y^7

Key Concepts

Properties of Exponents

The properties of exponents are rules that govern how to manipulate expressions involving powers. One key property is that when multiplying two expressions with the same base, you add their exponents. For example, a^m * a^n = a^(m+n). This principle is essential for simplifying expressions like (y^2)(y^5).

Simplifying Expressions

Simplifying expressions involves reducing them to their most basic form while maintaining equality. This process often includes combining like terms and applying the properties of exponents. In the case of (y^2)(y^5), simplifying requires using the exponent addition rule to find the correct exponent for y.

True or False Statements in Algebra

In algebra, determining whether a statement is true or false often involves verifying the equality of both sides of an equation. If the two sides do not match, the statement is false, and one must identify the correct form. For the equation (y^2)(y^5) = y^7, checking the left side against the right side reveals whether the statement holds true.