Question

Evaluate 3 root 2 . 4^3/2 ÷128 ^1/3

Answer 1

Answer:

1281/332×423

Step-by-step explanation:

the answer is 3

Answer 2

Concept

Product law of exponents

According to the law of the product of exponents, when multiplying two numbers that have the same base, we can add the exponents as

x^m.x^n = x^(m+n)

Quotient law of exponents

According to the quotient law of exponents, we can divide two numbers with the same base by subtracting the exponents.

x^m÷x^n = x^(m-n)

Product power rule

The product power rule states that:

(a×b)^n=a^n×b^n

The rule of the power of a quotient

The product power rule states that:

(a/b)^n=a^n/b^n

Given

3√2 * 4^3/2 ÷128 ^1/3 is given

Find

We need to find the value of 3√2 * 4^3/2 ÷128 ^1/3

Solution

(3 * 2^(1/2) *4^3/2 ) ÷128 ^1/3

(3 * 2^(1/2) * (2 ^2)^(3/2)) ÷ 2^(7/3)

(3 * 2^(1/2) * 2^3) ÷ 2^(7/3)

(3 * 2 ^(1/2 + 3) ÷ 2^(7/3) )

( 3 * 2 ^(7/2) ÷ 2^(7/3))

3 * 2^(7/2 - 7/3)

3 * 2^(7/6)

Hence the value of 3√2 * 4^3/2 ÷128 ^1/3 is 3 * 2^(7/6)

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