The power of a that makes it equal to b is x = 5/6
The square root of a number is a number when multiplied by itself gives another number.
The cube root of a number is a number when multiplied by itself three times gives another number.
The power of a number is the exponent of that number
Since two numbers, a and b, are each greater than zero, and 4 times the square root of a is equal to 9 times the cube root of b. It follws that
4√a = 9∛b
⇒∛b = 4√a/9
⇒ b = ∛[4√a/9]
Since we require the of x is a, to the x power equal to b if a = 2/3.
This implies that
aˣ = b
Substituting b into the equation, we have
aˣ = ∛[4√a/9]
Since a = 2/3, we have
(2/3)ˣ = ∛[4√(2/3)/9]
(2/3)ˣ = ∛[4/9 × √(2/3)]
(2/3)ˣ = ∛[2²/3² × √(2/3)]
(2/3)ˣ = ∛[(2/3)² × √(2/3)]
(2/3)ˣ = ∛[2/3)
[tex](\frac{2}{3} )^{x} = \sqrt[3]{(\frac{2}{3} )^{2 + \frac{1}{2}} } \\(\frac{2}{3} )^{x} = \sqrt[3]{(\frac{2}{3} )^{\frac{5}{2}} } \\(\frac{2}{3} )^{x} = (\frac{2}{3} )^{\frac{5}{2} \times \frac{1}{3} } \\(\frac{2}{3} )^{x} = (\frac{2}{3} )^{\frac{5}{6}[/tex]
Equating both powers, we see that x = 5/6
So, the power of a is x = 5/6
Learn more about powers of exponents here:
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