Question

What is the value of (9^7) ^3/14, in simplest terms? a0

Answer 1

Answer:

27.

Step-by-step explanation:

It is one property of exponents that for any numbers a, b, and c

$(a^b)^c=a^{bc}$

Therefore, using this property the expression  $(9^7) ^{3/14}$ becomes

$(9^7) ^{3/14} =9^{(7*\frac{3}{14} )}$.

and when when simplify the exponents, we get:

$9^{(\frac{21}{14} )}= 9^{\frac{3}{2} }= (9^{\frac{1}{2} })^3$.

Since for any number  $a^\frac{1}{2} =\sqrt{a}$ ( $\dfrac{1}{2}$ in the exponent means the square root) , $(9^{\frac{1}{2} })^3$ is rewritten as

$(\sqrt9} )^3$

which simplifies to

$(\sqrt9} )^3=3^3 =\bold{27}$

Thus,

$\boxed{ (9^7) ^{3/14}=27}$