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PLEASE SOLVE
Write 8x³y³ as the power of a product.

Sagot :

djtwinx017

Answer:

(2xy)³

Step-by-step explanation:

According to the Power Rule of Exponents:

[tex](ab})^{m} = a^{m}b^{m}[/tex]

We can apply the Power Rule of Exponents to the given exponential expression, 8x³y³, by taking the smallest factor that when cubed (or raised to an exponent of 3), will produce the same results as the original exponential expression.

8 is a perfect cube of 2:  ⇒  2 × 2 × 2 = 2³ = 8

The cube of x is x³:   ⇒  x × x × x = x³

The cube of y is y³  ⇒  y × y × y  = y³

Hence, we can take the least common factors, (2xy) and raise them to the third power:

(2xy)³ = 2³x³y³ =  8x³y³

Therefore, the correct answer is: (2xy)³

[tex]\\ \sf\longmapsto 8x^3y^3[/tex]

  • 8=2^3
  • x^3=(x)^3
  • y^3=(y)^3

We know the rule of exponents

[tex]\boxed{\sf (ab)^m=a^mb^m}[/tex]

Now

[tex]\\ \sf\longmapsto 8x^3y^3[/tex]

[tex]\\ \sf\longmapsto 2^3x^3y^3[/tex]

[tex]\\ \sf\longmapsto (2xy)^3[/tex]

[tex]\\ \sf\longmapsto (2xy)(2xy)(2xy)[/tex]

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