Problem 950 Determine the value of \((0.0081... [FREE SOLUTION]

Chapter 33: Problem 950

Determine the value of \((0.0081)^{-3 / 4}\).

Short Answer

Expert verified

The value of \((0.0081)^{-3/4} \approx 1371.74\).

Step by step solution

Rewrite the expression using the property of negative exponents

To handle the negative exponent, we can use the property of negative exponents which states that \(a^{-n} = \frac{1}{a^n}\). So we can rewrite the expression as: \[ (0.0081)^{-3/4} = \frac{1}{(0.0081)^{3/4}} \]

Rewrite 0.0081 with fractional exponent

Notice that 0.0081 can be written as the value 0.081 to the \(4^{th}\) power, so \(0.0081 = (0.081)^4\). We can substitute this into the expression from Step 1: \[ \frac{1}{(0.0081)^{3/4}} = \frac{1}{((0.09)^4)^{3/4}} \]

Use the power of a power rule

Now, we can simplify the expression using the power of a power rule, which states that \((a^m)^n = a^{mn}\). Applying this rule to the expression, we get: \[ \frac{1}{((0.09)^4)^{3/4}} = \frac{1}{(0.09)^{4 \cdot 3/4}} \]

Simplify the exponent

Now we can simply multiply the exponents to find the exponent of 0.09: \[ (0.09)^{4 \cdot 3/4} = (0.09)^3 \]

Calculate the value

Finally, we can calculate the value of the simplified expression: \[ \frac{1}{(0.09)^3} = \frac{1}{0.000729} \approx 1371.74 \] Therefore, the value of \((0.0081)^{-3/4} \approx 1371.74\).

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91影视

Determine the value of \((0.0081)^{-3 / 4}\).

Short Answer

Step by step solution

Rewrite the expression using the property of negative exponents

Rewrite 0.0081 with fractional exponent

Use the power of a power rule

Simplify the exponent

Calculate the value

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