Questions: Understanding the power rules of exponents Follow the instructions below. Write (2 b)^4 without exponents. (2 b)^4= Fill in the blanks. (2 b)^4= b^

Solution Steps

To solve the problem of writing \((2b)^4\) without exponents, we need to expand the expression by multiplying \(2b\) by itself four times. Then, we can use the power rule of exponents, which states that \((ab)^n = a^n \cdot b^n\), to separate the expression into powers of 2 and powers of \(b\).

To write \((2b)^4\) without exponents, we expand the expression by multiplying \(2b\) by itself four times: \[ (2b)^4 = 2b \times 2b \times 2b \times 2b \]

Using the power rule of exponents, \((ab)^n = a^n \cdot b^n\), we can separate the expression into powers of 2 and powers of \(b\): \[ (2b)^4 = 2^4 \times b^4 \]

Calculate \(2^4\): \[ 2^4 = 16 \] Thus, the expression becomes: \[ 16 \times b^4 \]

Final Answer