Question

using rational exponents to rewrite expressions - item 50623 which expression has the same meaning as ( sqrt{m^{16}} )? options: ( m^{\frac{1}{16}} ), ( m^{\frac{1}{8}} ), ( m^8 ), ( m^4 )

Explanation:

Step1: Recall the square root property

The square root of a number \( x \) can be written as \( x^{\frac{1}{2}} \). So, \( \sqrt{m^{16}}=(m^{16})^{\frac{1}{2}} \).

Step2: Apply the power - of - a - power rule

The power - of - a - power rule states that \( (a^{m})^{n}=a^{m\times n} \). For \( (m^{16})^{\frac{1}{2}} \), we have \( m^{16\times\frac{1}{2}} \).

Step3: Simplify the exponent

Calculate \( 16\times\frac{1}{2}=8 \). So, \( (m^{16})^{\frac{1}{2}} = m^{8} \).

Answer:

\( m^{8} \) (the option with \( m^{8} \))