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Sagot :

Answer:

312.5 t⁴

Step-by-step explanation:

25*t⁻⁴ = (5²) / t⁴     (1)

5⁻³*10*t⁻⁸ = 5⁻³*2*5¹ / t⁸   (2)

(1)/(2): ((5²) / t⁴) / ((5⁻²*2) / t⁸) = 5⁴ * t⁴ / 2 = 625 t⁴ / 2 = 312.5 t⁴

Answer:

[tex] \frac{625 {t}^{4} }{2} [/tex] or 312.5t⁴

Step-by-step explanation:

to understand this

you need to know about:

  • law of exponent
  • PEMDAS

given:

  • [tex] \frac{25 \times {t}^{ - 4} }{ {5}^{ - 3} \times 10 \times {t}^{ - 8} } [/tex]

tips and formulas:

  • [tex]x ^{a} \times {x}^{b } = {x}^{a + b} [/tex]
  • [tex] \frac{ {x}^{a} }{ {x}^{ b } } = {x}^{a - b} [/tex]

let's solve:

[tex] step - 1 : define\\ \frac{25 \times {t}^{ - 4} }{ {5}^{ - 3} \times 10 \times {t}^{ - 8} } [/tex]

[tex] step - 2: simplify\\ \frac{ {5}^{2} \times {t}^{ - 4} }{ {5}^{ - 3} \times 2.5\times {t}^{ - 8} } \\ \\ \frac{ {5}^{2} }{ {5}^{ - 3 + 1} } \times \frac{ {t}^{ - 4} }{ {t}^{ - 8} } \times \frac{1}{2} \\ {5}^{2 + 2} \times {t}^{ - 4 - ( - 8)} \times \frac{1}{2 } \\ 625 \times {t}^{4} \times \frac{1}{2} \\ \therefore \frac{625 {t}^{4} }{2} [/tex]

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