Question

Which expression is equivalent to

Answer 1

Answer:

The correct answer is option 2.

The equivalent of given expression is,  

3/5x⁶y⁶

Step-by-step explanation:

Identities:

xᵃ/xᵇ = x⁽ᵃ⁻ᵇ⁾

1/x-ᵃ=xᵃ

It is given that,

(-9x⁻¹y⁻⁹)/(-15x⁵y⁻³)

To find the equivalent expression

The expression is,

(-9x⁻¹y⁻⁴)/(-15x⁵y⁹)

By using the above identities we can write,

-9x⁻¹y⁻⁹/-15x⁵y⁻³ = 3/(5x⁽⁵⁺¹⁾y⁽⁹⁻³⁾)

since xᵃ/xᵇ = x⁽ᵃ⁻ᵇ⁾

1/x-ᵃ=xᵃ

-9x⁻¹y⁻⁹/-15x⁵y⁻³  = 3/5x⁶y⁶

Therefore the correct answer is second option.

3/5x⁶y⁶ is the equivalent fraction of given expression.

Answer 2

For this case, we must find an expression equivalent to:

$\frac {-9x ^ {- 1} y ^ {- 9}} {- 15x ^ 5y ^ {- 3}}$

By definition of power properties we have:

$a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}$

Rewriting the previous expression we have:

The "-" are canceled and we take into account that:

$\frac {9} {15} = \frac {3} {5}$

So:

$\frac {3} {5x^5 * x ^ 1 *y ^ 9* y ^ {- 3}} =$

According to one of the properties of powers of the same base, we must put the same base and add the exponents:

$\frac {3} {5x ^ {5 + 1} * y ^ {9-3}} =\\\frac {3} {5x ^ 6 * y ^ 6}$

Answer:

$\frac {3} {5x ^ 6 * y ^ 6}$

Option B