SIMPLIFICATION
(10c²/2d³)²
Step-by-step Solution:
[tex]{ \tt{( {\frac{ {10c}^{2} }{ {2d}^{3} } )}^{2} }}[/tex]
1. Factor 2 out of 10c^2.
[tex]{ \tt{ {( \frac{2( {5c}^{2}) }{ {2d}^{3} } )}^{2} }}[/tex]
2. Factor 2 out of 2d^3.
[tex]{ \tt{ {( \frac{2( {5c}^{2} )}{2( {d}^{3} )} )}^{2} }}[/tex]
3. Cancel the common factor.
[tex]{ \tt{ {( \frac{ \cancel{2}( {5c}^{2} )}{ \cancel{2}( {d}^{3} )} )}^{2} }}[/tex]
4. Rewrite the expression.
[tex]{ \tt{ {( \frac{ {5c}^{2} }{ {d}^{3} } )}^{2} }}[/tex]
5. Use the power rule (ab)^n = a^n b^n to distribute the exponent.
6. Apply the product rule to 5c^2/d^3.
[tex]{ \tt{ \frac{ { ({5c}^{2}) }^{2} }{ {( {d}^{3} )}^{2} } }}[/tex]
7. Apply the product rule to 5c^2.
[tex]{ \tt{ \frac{ {5}^{2}( {c}^{2})^{2} }{ {( {d}^{3} )}^{2} } }}[/tex]
8. Raise 5 to the power of 2.
[tex]{ \tt{ { \frac{25 ({c}^{2} )}{ {( {d}^{3}) }^{2} } }^{2} }}[/tex]
9. Apply the power rule and multiply exponents.
[tex]{ \tt{ \frac{ {25c}^{2 \times 2} }{ { {d}^{3 \times 2} } } }}[/tex]
10. Evaluate.
[tex]{ \tt{ \frac{ {25c}^{4} }{{ {d}^{6} } } }}[/tex]
Answer:
[tex]{ \color{blue}{ \boxed{ \color{blue}{ \huge{ \boxed{ \sf{ \frac{ {25c}^{4} }{ {d}^{6} } }}}}}}}[/tex]
==================
[tex]{ \color{purple}{ \underline{ \sf{ichthus898}}}}[/tex]
