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Exponents are a way of representing repeated multiplication of the same number. For instance, instead of writing out a long multiplication, like \(2 \times 2 \times 2 \times 2 \times 2\) (five times in total), we use the exponent form: \(2^5\). Here, the base number is \(2\), and the exponent (or power) is \(5\). The exponent tells us how many times to multiply the base by itself.
In the context of this exercise, we have an expression where the base is a variable \(y\) raised to an exponent. Specifically, it’s \( (y^2)^7\). Understanding how to manipulate these exponents is key to solving it.

When simplifying expressions that involve exponents, especially those that follow the power of a power rule, it's essential to follow the right steps. In our exercise, we start with the expression \( (y^2)^7\). To simplify this using the power of a power rule, we need to follow these rules:

• Identify the base and the exponents involved – in this case, \(y\) is the base, \(2\) is the first exponent, and \(7\) is the second exponent.
• Apply the power of a power rule, which states if you have \( (a^m)^n\), it simplifies to \( a^{m \times n}\). This means you multiply the two exponents.
• For our exercise, \(2 \times 7 = 14\). Therefore, \((y^2)^7 = y^{14}\).

Through these steps, it converts a seemingly complex expression into a much simpler one.

Pre-algebra is an essential foundation for your mathematics journey. It involves understanding basic mathematical concepts that are the building blocks for algebra and more advanced math. Key topics include arithmetic operations, basic equations, and properties of numbers.
In pre-algebra, you’ll encounter exponents frequently. It’s important to get comfortable with concepts like the power of a power rule, which we used in our exercise. Pre-algebra teaches you to handle these rules and apply them to simplify expressions.
Mastering these basics makes it easier when you move on to solving more complex algebraic equations and expressions. So, understanding how to simplify expressions like \( (y^2)^7\) is a crucial part of your learning process.