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In elementary algebra, exponents are a shorthand way of writing repeated multiplication. For example, the expression \(x^4\) means you multiply the variable \(x\) by itself four times. Similarly, \(y^6\) means multiplying \(y\) by itself six times. To 'remove exponents,' we need to rewrite these expressions without using the exponent notation. This is done by expanding each term into its multiplication form.

So, for \(x^4\), we write it as \(x \times x \times x \times x\). Similarly, we write \(y^6\) as \(y \times y \times y \times y \times y \times y\). Removing exponents helps give a clearer view of how many times each variable is being multiplied, which is fundamentally helpful in understanding algebra.

Expanding expressions is a process where we break down a term with an exponent into its basic multiplication form. For instance, \(x^4\) can be expanded as \(x \times x \times x \times x\). This means you multiply the base (\(x\)) by itself four times.

In our given problem, we have two terms: \(x^4\) and \(y^6\). We need to expand both:

• For \(x^4\): The expansion is \(x \times x \times x \times x\)
• For \(y^6\): The expansion is \(y \times y \times y \times y \times y \times y\)

Expanding these terms helps visualize the multiplication involved and provides a way to see the nitty-gritty of the expression.

Multiplying variables in algebra involves taking the base variable and repeatedly combining it by following the rules of multiplication. When we deal with exponents, such as \(x^4\) or \(y^6\), multiplication means expanding and then combining the terms.

Consider our example again:

• \(x^4 = x \times x \times x \times x\)
• \(y^6 = y \times y \times y \times y \times y \times y\)

When multiplying variables with the same base, we essentially add the exponents. But here, since we’re just expanding, we write each term out without using the exponent notation. This practice of expanding and visualizing each multiplication improves our fundamental understanding of algebraic expressions.