Question

which of the following is equal to the fraction below? (7/4)^ 11

Answer 1

When you multiply an exponent directly into another exponent, you multiply the exponents

(for a fraction, you multiply the exponent to both the numerator and denominator)

For example:

$(x^{2})^5=x^{2(5)}=x^{10}$

$(\frac{x^3}{y^2} )^5=\frac{x^{3(5)}}{y^{2(5)}} =\frac{x^{15}}{y^{10}}$

$(\frac{7}{4})^{11}=(\frac{7^1}{4^1})^{11}=\frac{7^{11}}{4^{11}}$

Your answer is A

Answer 2

Answer:

$(\frac{7^{11}}{4^{11}})$

Step-by-step explanation:

$(\frac{7}{4})^{11}$

To simplify this fractional exponent we apply exponential property

$(\frac{x}{y})^m=\frac{x^m}{y^m}$

As per this property , we multiply the exponent inside the fraction

Multiply the exponent 11 inside the fraction

Multiply the exponent 11 with 7 and then 4

$(\frac{7}{4})^{11}$

$(\frac{7^{11}}{4^{11}})$