Question

Write 32^(-(2)/(5)) without using exponents or radicals.

Answer 1

To write 32^(-(2)/(5)) without using exponents or radicals, we can express it as a fraction. The denominator of the fraction represents the root, and the numerator represents the number being raised to that root. So, the fraction -(2)/(5) means we want to take the fifth root of 32, and then negate that result. The fifth root of 32 is 2, so the final answer is -2.

Step-by-step explanation:

To write 32^(-(2)/(5)) without using exponents or radicals, we can express it as a fraction. The denominator of the fraction represents the root, and the numerator represents the number being raised to that root. So, the fraction -(2)/(5) means we want to take the fifth root of 32, and then negate that result. The fifth root of 32 is 2, so the final answer is -2.

Answer 2

`\(32^{-(2)/(5)}\)` can be written as
`\(2^(-2)\).`

Expressing 32 as
`\(2^5\)`: 32 is equal to
`\(2^5\)` because
`\(2 * 2 * 2 * 2 * 2 = 32\)`.

Using Laws of Exponents: When you have a power raised to another power, you can multiply the exponents. So,
`\((a^m)^n = a^(m * n)\)`.

Applying this to
`\((2^5)^{-(2)/(5)}\)`, you multiply the exponents:
`\(5 * -(2)/(5) = -2\)`.

Solving the Exponent: means the reciprocal of
`\(2^2\) or \((1)/(2^2)\)`, which simplifies to
`\((1)/(4)\).`

So,
`\(32^{-(2)/(5)}\)` is equal to
`\(2^(-2)\),` which simplifies to
`\((1)/(4)\).`