Question

(b^9/16)^2 : b^1/8 при b =12

Answer 1

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Answer 2

To simplify the expression $\left(\frac{b^{\frac{9}{16}}}{b^{\frac{1}{8}}}\right)^2$ and calculate it when $b = 12$, we follow these steps:

Step 1: Apply the quotient of powers rule. When you have the same base and are dividing, subtract the exponents:

$\frac{b^{\frac{9}{16}}}{b^{\frac{1}{8}}} = b^{\frac{9}{16} - \frac{1}{8}}$

Step 2: Simplify the exponent:

$b^{\frac{9}{16} - \frac{1}{8}} = b^{\frac{9}{16} - \frac{2}{16}} = b^{\frac{7}{16}}$

Step 3: Square the result:

$\left(b^{\frac{7}{16}}\right)^2 = b^{\frac{7}{8}}$

Now, we substitute $b = 12$ into the simplified expression:

$b^{\frac{7}{8}} = 12^{\frac{7}{8}}$

Now, calculating $12^{\frac{7}{8}}$ can be done as follows:

$12^{\frac{7}{8}} = \left(\sqrt[8]{12}\right)^7$

Using a calculator to evaluate $\sqrt[8]{12}$, we get approximately 1.669. Now, raise it to the power of 7:

$1.669^7 \approx 49.97$

Therefore, $\left(\frac{b^{\frac{9}{16}}}{b^{\frac{1}{8}}}\right)^2$ is approximately $49.97$ when $b = 12$.