# How do you evaluate c^ -3(16^ -2) for c=4?

Mar 22, 2016

=color(green)(4^-7

#### Explanation:

${c}^{-} 3 \left({16}^{-} 2\right)$ , color(blue)(c=4

Substituting the value of $c$ given:

$= \textcolor{b l u e}{{4}^{-} 3} \left({16}^{-} 2\right)$

note: $16$ can be written as ${4}^{2}$

$= \textcolor{b l u e}{\left({4}^{-} 3\right)} \left({4}^{2 \cdot \left(- 2\right)}\right)$

$= \textcolor{b l u e}{\left({4}^{-} 3\right)} \left({4}^{-} 4\right)$

• by property
color(blue)(a^m * a^n = a^(m+n)

color(blue)((4^ - 3)) (4^ -4) = 4^(( -3 + ( -4))

=color(green)(4^-7
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 12, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}