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(y ^ 4 * y ^ n)/(y ^ 2) = y ^ - 3 Find the value of n. (2 marks)

Sagot :

semsee45

Answer:

n = -5

Step-by-step explanation:

Given:

  [tex]\dfrac{y^4 \cdot y^n}{y^2}=y^{-3}[/tex]

Multiply both sides by y²:

[tex]\implies \dfrac{y^4 \cdot y^n}{\diagup \!\!\!\!\!y^2} \cdot \diagup \!\!\!\!\!y^2=y^{-3}\cdot y^2[/tex]

[tex]\implies y^4 \cdot y^n=y^{-3} \cdot y^2[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies y^{4+n}=y^{-3+2}[/tex]

[tex]\implies y^{4+n}=y^{-1}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]

[tex]\implies 4+n=-1[/tex]

Solve for n by subtracting 4 from both sides:

[tex]\implies 4+n-4=-1-4[/tex]

[tex]\implies n=-5[/tex]

mhanifa

Answer:

  • n = - 5

===========

Given equation:

  • [tex]\dfrac{y^4*y^n}{y^2} =y^{-3}[/tex]

Solve it for n:

  • [tex]y^{4+n-2}=y^{-3}[/tex]      
  • [tex]y^{2+n}=y^{-3}[/tex]
  • [tex]2+n=-3[/tex]
  • [tex]n=-3-2[/tex]
  • [tex]n=-5[/tex]

===========

Used properties:

  • [tex]a^b*a^c=a^{b+c}[/tex]                  product of exponents with same base
  • [tex]a^b/a^c=a^{b-c}[/tex]                    division of exponents with same base
  • If [tex]a^b=a^c[/tex]  then [tex]b = c[/tex]       equal exponents with same base

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