The answer is:
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a = " [tex] \frac{13}{4} [/tex] " ; or; write as: " 3 [tex] \frac{1}{4} [/tex] " ;
→ or; write as: " 3.25 " .
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Explanation:
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GIven: " x^{2} * \sqrt[4]{x^{5} } = x^{a} " ;
Solve for "a" ; using the "properties of exponents" .
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Note: " ⁴√(x⁵) = [tex] x^{ \frac{5}{4}} [/tex] " .
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Note that: " 2 = [tex] \frac{8}{4} [/tex] " .
[tex] x^{2} [/tex] * tex] x^{ \frac{5}{4}} [/tex] =
[tex]x^{2+ \frac{5}{4}} =x^{ \frac{8}{4}+\frac{5}{4} }=x^{ \frac{(8+5)}{4}} [/tex] ;
→ [tex] x^{ \frac{(8+5)}{4} } = x^{ \frac{13}{4} } ;
→ x^{ \frac{13}{4} } = x^{a} [/tex] ;
↔ x^{a} [/tex] = x^{ \frac{13}{4} } ;
Solve for "a" ;
→ a = " [tex] \frac{13}{4} [/tex] " ; or; write as: " 3 [tex] \frac{1}{4} [/tex] " ;
or; write as: " 3.25" .
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