Question

Which expression is equivalent to StartFraction 5 y cubed Over (5 y) Superscript negative 2 Baseline EndFraction? y5 y6 125y3 125y5

Answer 1

Answer:

the answer is d

Step-by-step explanation:

Answer 2

Answer:

The expression which is equivalent to the fraction is $125y^{5}$ ⇒ 4th answer

Step-by-step explanation:

Let us revise some rules of exponents

$a^{m}$ × $a^{n}$ = $a^{m+n}$

$a^{m}$ ÷ $a^{n}$ = $a^{m-n}$

$(a^{m})^{n}$ = $a^{m.n}$

$(a.b)^{n}$ = $a^{n}$ × $b^{n}$

∵ The fraction is  $\frac{5y^{3} }{(5y)^{-2}}$

∵ $(5y)^{-2}$ = $5^{-2}$ × $y^{-2}$ ⇒ 4th rule

∴  $\frac{5y^{3} }{(5y)^{-2}}$  =  $\frac{5.y^{3} }{5^{-2}.y^{-2} }$

- The base line of the fraction means ÷, so let us use the

  2nd rule above

∵ 1 - (-2) = 1 + 2 = 3

∵ 3 - (-2) = 3 + 2 = 5

∴  $\frac{5^{1} }{5^{-2}}$ = $5^{1--2}$

∴  $\frac{5^{1} }{5^{-2}}$ = $5^{3}$

∴  $\frac{y^{3} }{y^{-2}}$ = $y^{3--2}$

∴   $\frac{y^{3} }{y^{-2}}$ = $y^{5}$

∴  $\frac{5y^{3} }{(5y)^{-2}}$  = $5^{3}.y^{5}$

∵ 5³ = 125

∴ $\frac{5y^{3} }{(5y)^{-2}}$  = $125y^{5}$

The expression which is equivalent to the fraction is $125y^{5}$