Question

(-7)^5/3 x (1/56)^5/3 Evaluate

Answer 1

The value of expression
`$$(-7)^{(5)/(3)}\cdot((1)/(56))^{(5)/(3)`
`$$(-7)^{(5)/(3)}\cdot((1)/(56))^{(5)/(3)` is
`-(1)/(32)$$`.

Let's evaluate the expression in the image:

`$$(-7)^{(5)/(3)}\cdot((1)/(56))^{(5)/(3)}$$`

We can simplify the expression using the following properties of exponents:

`$x^m \cdot x^n = x^(m+n)$`

`$\left((x)/(y)\right)^m = (x^m)/(y^m)$`

Simplify the expression:

`$$(-7)^{(5)/(3)}\cdot((1)/(56))^{(5)/(3)} = (-7)^{(5)/(3)}\cdot((1)/(2^3 \cdot 7))^{(5)/(3)}$$`

`$$= (-7)^{(5)/(3)}\cdot(2^(-3) \cdot 7^(-1))^{(5)/(3)}$$`

Apply the exponent properties:

`$$= (-7)^{(5)/(3)}\cdot 2^{(-3)\cdot(5)/(3)}\cdot 7^{(-1)\cdot(5)/(3)}$$`

`$$= -7^{(5)/(3)}\cdot 2^(-5)\cdot 7^{-(5)/(3)}$$`

Simplify further:

`$$= (-1 \cdot 7)^{(5)/(3)}\cdot 2^(-5)\cdot 7^{-(5)/(3)}$$`

`$$= -1\cdot 7^{(5)/(3)}\cdot 2^(-5)\cdot 7^{-(5)/(3)}$$`

`$$= -1\cdot 7^{{(5)/(3)}-{(5)/(3)}}\cdot 2^(-5)$$`

`$$= -1\cdot 1\cdot 2^(-5)$$`

`$$= -2^(-5)$$`

Convert negative power to positive:

`$$= -(1)/(2^(5))$$`

Calculate the final answer:

`$$= -(1)/(32)$$`

Answer 2

To evaluate the expression (-7)^5/3 x (1/56)^5/3, break the expression down, apply the exponent to both -7 and 1/56, and finally express the negative result in proper scientific notation.

Step-by-step explanation:

The question involves evaluating the expression (-7)5/3 × (1/56)5/3. To solve this, you must first break it down into two parts: raising -7 and 1/56 each to the power of 5/3. To raise a negative number to an odd fractional exponent, the result is negative. For 1/56, you will raise both numerator and denominator to the 5/3 power. After computing, both results will be multiplied together.

Since both the constants -7 and 56 have the same exponent, we can combine them under a single exponent like this: ((-7)/56)5/3. You would then calculate by raising -1/8 to the power of 5/3, which simplifies the computation. The final answer can be expressed in proper scientific notation, with a sign to indicate it is a negative result.