Question

follow the instructions below. write ((6a)^2) without exponents. ((6a)^2 = square) fill in the blanks. ((6a)^2 = square a^{square})

Explanation:

Step1: Apply exponent rule

Using the power of a product rule \((xy)^n = x^n y^n\), for \((6a)^2\), we have \(6^2\times a^2\).

Step2: Calculate \(6^2\)

\(6^2 = 6\times6 = 36\), and \(a^2=a\times a\). So \((6a)^2 = 36\times a\times a=36a^2\) (but for the first blank without exponents in the sense of expanding the square, it's \(6a\times6a\), and for the fill - in - the - blanks, we know that \((6a)^2=6^2\times a^2 = 36a^2\), so the first blank in the first part is \(6a\times6a\), and in the second part, the first box is \(36\) and the second box is \(2\)).

For the first equation \((6a)^2=\square\) (writing without exponents by expanding the square):

Step1: Recall the meaning of squaring a product

Squaring a quantity means multiplying it by itself. So \((6a)^2\) means \(6a\) multiplied by \(6a\).

Step2: Write the expansion

\((6a)^2=6a\times6a\)

For the second equation \((6a)^2=\square a^{\square}\):

Step1: Apply the power of a product rule

The power of a product rule states that \((xy)^n=x^n\times y^n\). Here \(x = 6\), \(y=a\) and \(n = 2\). So \((6a)^2=6^2\times a^2\).

Step2: Calculate \(6^2\)

\(6^2=6\times6 = 36\). So \((6a)^2 = 36a^2\), which means the first blank is \(36\) and the second blank is \(2\).

First part answer: \(6a\times6a\)

Second part answer: The first box is \(36\) and the second box is \(2\)

(If we consider the first part's answer as the expanded form without using exponents to represent the square, and the second part as the simplified form with the coefficient and the exponent on \(a\))

Answer:

For \((6a)^2=\square\) (expanded form): \(6a\times6a\)

For \((6a)^2=\square a^{\square}\): The first blank is \(36\), the second blank is \(2\) (i.e., \((6a)^2 = \boldsymbol{36}a^{\boldsymbol{2}}\))